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Paper Citation Record · LEDGER

A Minkowski problem for $\alpha$-concave functions via optimal transport

As of 18 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 1 inbound Pith citation observation for arXiv:2506.14735.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.14735 v2

Coverage vector

measured 63 of 63 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:01:34.423751Z

measured 64 of 64 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T17:28:49.682827Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-15T17:28:49.884655Z

Reference resolution

63 of 63 outbound references displayed

  • verified exact0
  • verified fuzzy30
  • unresolved33
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1dbf2c59-6166-4f88-aa80-aedb230e3522 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:35.096862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.209775Z digest=sha256:1f745c95c2d0bddf9cb8bed1038936e119b62634607e887aa45c27dc98a2be85

Observation 6d32ad53-2bce-4726-9636-1238ed107317 · outbound

This paper cites H., Villa, R.:Rogers-Shephard and local Loomis–Whitney type inequalities.

A Minkowski problem for $\alpha$-concave functions via optimal transport H., Villa, R.:Rogers-Shephard and local Loomis–Whitney type inequalities

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:35.086722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 41cb432e-ab58-4b12-8b09-038574142e8b · outbound

This paper cites H., Villa, R.:Rogers–Shephard inequality for log- concave functions.

A Minkowski problem for $\alpha$-concave functions via optimal transport H., Villa, R.:Rogers–Shephard inequality for log- concave functions

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:35.076285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 78fb0341-2451-4812-bcbd-2fc58e911a2a · outbound

This paper cites H., Villa, R.:John’s Ellipsoid and the Integral Ratio of a Log-Concave Function.

A Minkowski problem for $\alpha$-concave functions via optimal transport H., Villa, R.:John’s Ellipsoid and the Integral Ratio of a Log-Concave Function

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:35.065863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.221910Z digest=sha256:dca90aec46e3a58bff55cd336704064c07d3de786df70ce32453b81c3740b8b2

Observation b69ec3eb-5724-41b2-a136-48f89f308db6 · outbound

This paper cites 51, 33-48 (2004).

A Minkowski problem for $\alpha$-concave functions via optimal transport 51, 33-48 (2004)

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:35.054683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.225550Z digest=sha256:1119d5b4afcfb403a82645357c8d3856f9ab15eef4bdebc341692cf81d416fc5

Observation b83bd834-8246-4656-92b9-fe3bc496e509 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:35.043821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.229134Z digest=sha256:68574c3e0e4b72f4fbe918622d646066de7b284643d05b43830903ad2e9252ef

Observation 8e0f8a53-64ab-4c85-8599-ac29d94d85f0 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:35.033144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.232930Z digest=sha256:bfe324032666eb9b95390526b31dc9300912a6a0209aa5e523d5fdaf75fd31c6

Observation e78d6671-a436-4d98-afe6-d99b407ce61e · outbound

This paper cites J., Colesanti, A., Yang, D.: The Lp-Minkowski problem for −n < p <1.

A Minkowski problem for $\alpha$-concave functions via optimal transport J., Colesanti, A., Yang, D.: The Lp-Minkowski problem for −n < p <1

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:35.021188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.236383Z digest=sha256:ab6bbc3df678758424bd0d9647d476ec932a2ed630778a46390b2fb52bfe0785

Observation e264d5d5-56cc-4d85-91a6-87f832ff86c2 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:35.010101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.240168Z digest=sha256:ed319add4d961babfe15f6a1fcc0916352ef404d10fcf1e56161a0fe9450cb7a

Observation f01ac56e-456a-4ac7-b393-03102d0f206d · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.999283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.243723Z digest=sha256:10eab946d4fa7a60c19649c39f503f5ae909750e6156c307bd78724ebf46b5d7

Observation b0c3174d-f6ef-44a4-8827-b2182fa6e338 · outbound

This paper cites J., Lutwak, E., Yang, D., Zhang, G.:The logarithmic Minkowski problem.

A Minkowski problem for $\alpha$-concave functions via optimal transport J., Lutwak, E., Yang, D., Zhang, G.:The logarithmic Minkowski problem

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.988744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 8f1e9a0e-3860-443a-9730-70c70797ee68 · outbound

This paper cites J., Lutwak, E., Yang, D., Zhang, G., Zhao, Y.:The Gauss Image Problem.

A Minkowski problem for $\alpha$-concave functions via optimal transport J., Lutwak, E., Yang, D., Zhang, G., Zhao, Y.:The Gauss Image Problem

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.978413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.251208Z digest=sha256:07245d6ac4c742f3dd538f3fea391b06d22c5d4afb65f83d4999682ba4bf768d

Observation 7224dd24-dd47-4f17-8ae4-8e6cba7104c6 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.968135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 431b5a42-d29b-40ca-8d6d-686a939c0c48 · outbound

This paper cites J., Lieb, E.

A Minkowski problem for $\alpha$-concave functions via optimal transport J., Lieb, E

Reference 14

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.258026Z digest=sha256:4478cec6922c7afe38d633c5ca4d414dde1880a8a229dfe5b3949a082f875e39

Observation c287aac7-d798-487c-b47f-ea66b8ea0a7f · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.947219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.260980Z digest=sha256:93cffde3f6d281b71e1b41c7e572f878571bce1e6a401c044f88bf36c97f407f

Observation 3b63078c-a3b6-444d-ad5e-3568bb9faa9d · outbound

This paper cites M.:Functional Versions ofLp-Affine Surface Area and Entropy Inequalities.

A Minkowski problem for $\alpha$-concave functions via optimal transport M.:Functional Versions ofLp-Affine Surface Area and Entropy Inequalities

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.936422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.264025Z digest=sha256:fd67b6580990b3657f81cb80912ba3c7c42f8ba7a4601ca37c8bc35d430f832d

Observation df6d71b6-2a2b-43da-a67d-37f81b772dc9 · outbound

This paper cites M.: Divergence for s-concave and log concave functions.

A Minkowski problem for $\alpha$-concave functions via optimal transport M.: Divergence for s-concave and log concave functions

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.925406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation db17ed7c-a452-41dc-9092-e878540b5b5e · outbound

This paper cites M.: Mixed f-divergence and inequalities for log-concave functions.

A Minkowski problem for $\alpha$-concave functions via optimal transport M.: Mixed f-divergence and inequalities for log-concave functions

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.914537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 4739e989-21d2-4aac-8ebc-1721860a6ea4 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.903418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 3aa65332-5380-46be-9de3-438e8fbbf079 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.893900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation d6511d0e-feb9-41ef-91a8-c9ffffbc9e12 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.884466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 74588758-13eb-47d6-af59-91922fee82d4 · outbound

This paper cites Cambridge University Press, Cambridge, (2019).

A Minkowski problem for $\alpha$-concave functions via optimal transport Cambridge University Press, Cambridge, (2019)

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.874129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 1c782833-6005-4b18-93a5-2b41e09b9430 · outbound

This paper cites On the functional Minkowski problem.

A Minkowski problem for $\alpha$-concave functions via optimal transport On the functional Minkowski problem

Reference 23

Resolution
unresolved
no resolver link, observed 2026-08-15T20:01:34.286738Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T20:01:34.286738Z digest=sha256:9c108ef09e86b0cbd158e0bc2865c6f3c3967df685b0dd21b0def29ce4484824

Observation 9d216271-2d1f-4d6f-ac51-5b63a6da19bd · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.864209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f02d848f-f384-49d1-bd9b-926d1c4818df · outbound

This paper cites The Riesz $\alpha$-energy of log-concave functions and related Minkowski problem.

A Minkowski problem for $\alpha$-concave functions via optimal transport The Riesz $\alpha$-energy of log-concave functions and related Minkowski problem

Reference 25

Resolution
unresolved
no resolver link, observed 2026-08-15T20:01:34.293718Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 68bbda01-1ce9-4f02-9992-0885172b0418 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.854325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 054a599a-820b-4ea9-adaa-30765c5eb665 · outbound

This paper cites EMS Press, Berlin, (2021).

A Minkowski problem for $\alpha$-concave functions via optimal transport EMS Press, Berlin, (2021)

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.843736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 64e20eb2-2ae0-4a55-b4ab-552cd850b604 · outbound

This paper cites B.: Real Analysis: Modern Techniques and Their Applications.

A Minkowski problem for $\alpha$-concave functions via optimal transport B.: Real Analysis: Modern Techniques and Their Applications

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.833591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation b26d2d97-2cd4-48c2-a4dc-132233725ddb · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.823690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation d0d022ab-4881-4c6d-acf9-cecec50df4e8 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.813314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation eaec1a21-aafd-45c1-ba4d-6548d3665efe · outbound

This paper cites J.: The geometry of optimal transportation.

A Minkowski problem for $\alpha$-concave functions via optimal transport J.: The geometry of optimal transportation

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.803350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 7ef6a831-c41a-4a21-8b44-65f626b4abff · outbound

This paper cites J., Hug, D., Weil, W., Xing, S., Ye, D.: General volumes in the Orlicz-Brunn–Minkowski theory and a related Minkowski problem I.

A Minkowski problem for $\alpha$-concave functions via optimal transport J., Hug, D., Weil, W., Xing, S., Ye, D.: General volumes in the Orlicz-Brunn–Minkowski theory and a related Minkowski problem I

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.793341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 0f91e70e-ec7f-4b5e-9ba4-ee535f6af2de · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.783565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f83a8064-4447-4732-9cbd-af5b5bc3344a · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.774406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 54ed2104-b0b8-4923-8e80-35ef1000f791 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.764892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.326696Z digest=sha256:4d550e2c6f42f306c32cbf2eba423d338c5e5229433a9cb06e5f0c6e755f393d

Observation 46674ae5-1e6d-44a6-8d66-54f43795073e · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.754919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.330272Z digest=sha256:045f7d0e3102f48b1491ad64017814c4e6963627845c99bdf839e9f7df563fcd

Observation e936c503-28d8-4555-8d0d-7d03a5270ca1 · outbound

This paper cites Journal of Convex Analysis.

A Minkowski problem for $\alpha$-concave functions via optimal transport Journal of Convex Analysis

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.742818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.333776Z digest=sha256:e1bafb83cb9f3d09dbbb3f0318cf2a35e91e5db4d0cca29b0ec73506f97bf318

Observation bc5c1bf5-fdc0-468b-b01a-a71b239932e3 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.732108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.337115Z digest=sha256:8087d6c906588bb1c469969749e054dc4b050aa257b773dbc53ac86db5771368

Observation 85384088-b909-48a2-91d0-beffc899e682 · outbound

This paper cites D.: Geometry of Log-concave Functions and Measures.

A Minkowski problem for $\alpha$-concave functions via optimal transport D.: Geometry of Log-concave Functions and Measures

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.722002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.340539Z digest=sha256:6eaa06218d842f8fe7cd1688f1f5e32071565af3e141e8d12190ff3da7a78ff2

Observation 1a2f5b9b-dd4c-41fa-9b38-826d0d654a44 · outbound

This paper cites S.: On the optimal mapping of distributions.

A Minkowski problem for $\alpha$-concave functions via optimal transport S.: On the optimal mapping of distributions

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.711412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.344027Z digest=sha256:c4a992e95f62fa7cd352657093e5c42a0d358e2e26f95d9d0f636dce7ad750b4

Observation 91c35c98-0a82-4dd9-b923-882b1226de55 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.701220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.347647Z digest=sha256:8ff8e2761d218524fd756ee2756981338ed723daf74e7fccf9751dc532f50b36

Observation 01e1fb0e-7634-4196-89c5-25e8f9ada935 · outbound

This paper cites M.: Floating functions.

A Minkowski problem for $\alpha$-concave functions via optimal transport M.: Floating functions

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.690676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.350966Z digest=sha256:636c88cfb560f977a5e694672ddb7a55c60a02ad5655b0059b8220bfe48abfc8

Observation 3356c1a2-60a2-4b1a-80d5-e54ba055771f · outbound

This paper cites M.: The L¨ owner Function of a Log-Concave Function.

A Minkowski problem for $\alpha$-concave functions via optimal transport M.: The L¨ owner Function of a Log-Concave Function

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.680352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.354402Z digest=sha256:95a3ce7b0864a1bc3d7cd8849565d5c88b2531fcca9adb26972652fd20bca9b2

Observation 13d66777-3da1-40a3-bbec-5b34206363d2 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.669997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.358014Z digest=sha256:6dfe35b409ef00f34c8fb4cc12b09ee83348af8df47cc86b7d4fa0b25721cbd5

Observation 1f48668e-7d35-4742-a2c9-808c036877b8 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.660089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.361329Z digest=sha256:d4b9bc8d3f92276346a3b858c9ae61d3f450c87956d3b30a42690b8d66dd36f5

Observation b067f036-ca51-4d0d-949a-72b7289901ef · outbound

This paper cites J.: Polar factorization of maps on Riemannian manifolds.

A Minkowski problem for $\alpha$-concave functions via optimal transport J.: Polar factorization of maps on Riemannian manifolds

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.650295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.364575Z digest=sha256:92cc68443d56a9e4ebaccc947a3ddf9bbf4d9a875cf45128a550a633e5632130

Observation f731b2ba-b665-46db-a43c-cd898240f297 · outbound

This paper cites Electron.

A Minkowski problem for $\alpha$-concave functions via optimal transport Electron

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.641097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.368208Z digest=sha256:befa951d761df6a2f4a5a15f1eb1ed1c44bf814fab18d94420b859310c3b6f5a

Observation b5cf5f4c-abfe-4dbd-abaf-1edf42dd3ffa · outbound

This paper cites (ed.) Ausgew¨ ahlte Arbeiten zur Zahlentheorie und zur Geometrie: Mit D.

A Minkowski problem for $\alpha$-concave functions via optimal transport (ed.) Ausgew¨ ahlte Arbeiten zur Zahlentheorie und zur Geometrie: Mit D

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.631227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.371601Z digest=sha256:8bf1b93dc8c67dcee7d8c04e8183753392d1fa62995f4c2c244b27e0c74f1ba2

Observation f37b2aee-32de-4cf4-9bed-4996abc927c5 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.609717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.379225Z digest=sha256:7b0688f30fb9a060f2dc535d5a79a1d60676aa68de9092503ce0cda3e4fb7d6c

Observation e197fb18-146f-47ac-acea-c54d744c87c6 · outbound

This paper cites T.: Convex Analysis.

A Minkowski problem for $\alpha$-concave functions via optimal transport T.: Convex Analysis

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.599928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.382654Z digest=sha256:7430e2637d8ce7ab52b8fe5d326027bec157f7d226a7ea97e9be21d25690797d

Observation 9d5a7eda-4d4e-4de9-9a2f-f8949b8e1a76 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.589775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.386481Z digest=sha256:25461f58ab19a3efc6c5082f7583cae038f0a14a58c2c32a6aea4236c0e8412e

Observation e8a24578-a47d-4c59-a1d1-2e53d0eec540 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.579543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.389803Z digest=sha256:9f6962e102fadc477b1e84657447cb2094e4466b0d7f5b7b1c634313f0fe8811

Observation 05bcaf6d-dd44-406d-b168-27bf0866f0b6 · outbound

This paper cites In: Eldan, R., Klartag, B., Litvak, A., and Milman, E.

A Minkowski problem for $\alpha$-concave functions via optimal transport In: Eldan, R., Klartag, B., Litvak, A., and Milman, E

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.569778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.393042Z digest=sha256:ef8ecc2fb62ea6f3e85cde0e4d26dd4a7fdb8b1ad2deda1c1953821db6a1952b

Observation 9d265807-3c7a-4242-b0ad-6564794d1420 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 54

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.559721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.396295Z digest=sha256:8aa498c94108e7782c68964473cf5dbf7e62cb48a43037aaf548dafaee63cbc0

Observation 9ccf0722-74ef-40f6-963c-d61ba2ceff7a · outbound

This paper cites Birkh¨ auser/Springer, Cham, (2015).

A Minkowski problem for $\alpha$-concave functions via optimal transport Birkh¨ auser/Springer, Cham, (2015)

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.548697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.399585Z digest=sha256:5c525dd18b6126af837bdc4281c92686ad1a99fdff83273467e41126d1eb8533

Observation b34ac6bb-ab5b-4603-8062-0b731e853e18 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 56

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.538119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.403005Z digest=sha256:83f32c3623929b5b662a457f596db4536745af671c47055f0f5fd367e48aa899

Observation 66d035d0-67ce-4879-b558-ff80dd8d9e03 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 57

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.526955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.406288Z digest=sha256:e08f6bbfd5183d8745a6efa3d3036a693f549d74651496c0722992cfef0de1a3

Observation 80a87603-b2b1-44d3-a591-8eb1a9930f76 · outbound

This paper cites First variation of functional Wulff shapes.

A Minkowski problem for $\alpha$-concave functions via optimal transport First variation of functional Wulff shapes

Reference 58

Resolution
unresolved
no resolver link, observed 2026-08-15T20:01:34.409642Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T20:01:34.409642Z digest=sha256:acac57de3eded66481c3d1e86171d154e9aedb809aa5897bffe7aee2f4b453b4

Observation 70bb6620-f8c3-4dcc-9231-e31fa6228b7a · outbound

This paper cites American Mathematical Society, Providence, RI, (2003).

A Minkowski problem for $\alpha$-concave functions via optimal transport American Mathematical Society, Providence, RI, (2003)

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.517223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.413596Z digest=sha256:181b41d6f9700c3fdc198dc42a551519baa7c3c6c9e5752ebac5c3d35fead9ba

Observation bba889ec-7ac4-450c-9efd-e0bffe1b33a0 · outbound

This paper cites Springer-Verlag, Berlin, (2009).

A Minkowski problem for $\alpha$-concave functions via optimal transport Springer-Verlag, Berlin, (2009)

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.507185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.416712Z digest=sha256:a85afb525a603551a45e10ba3ec8b38603cc4c7161df4bd2500302f9b909daae

Observation 767f8b0e-4229-41b9-9113-5f37b7da2d45 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 61

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.496727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.420145Z digest=sha256:7f394412cb3636ebaa9b2354f8790b36ad0ab8c5ae80ae2a7fc267231f69b35f

Observation 74507792-1dd4-41da-849b-13f0eb473935 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 62

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.485802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.423751Z digest=sha256:e7d5e1365ad4bcf95736723eaebbb333e96c833b36c1345632dbc91cc30b5eea

Observation dcc4817d-d5b0-45b7-84fe-f29455e2f204 · outbound

This paper cites Springer, Vienna (1989).

A Minkowski problem for $\alpha$-concave functions via optimal transport Springer, Vienna (1989)

Reference 1909

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.620491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T20:01:34.375602Z digest=sha256:d8b14653cfbd1c70041dc49b2aaba4803223622c21ecb33103e84331c4106b12

Pith citing papers

Observation 0905cf9a-f6f3-4787-b3f0-7d098580ce4f · inbound

The Gaussian Minkowski problem for epigraphs of convex functions cites this paper.

The Gaussian Minkowski problem for epigraphs of convex functions A Minkowski problem for $\alpha$-concave functions via optimal transport

Reference 20

Resolution
verified exact
local_arxiv, observed 2026-08-15T17:28:49.889581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=arxiv_source observed=2026-08-15T17:28:49.682827Z digest=sha256:4c4aa5cc99d2014e232c6e24cd1d74f660ecda2f6cc23e4d21f1cf9595701b58