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Paper Citation Record · LEDGER

An Alexandrov-type theorem in warped product manifolds with radial density

As of 19 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:2608.08548.

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

pith.paper-citation-record.v1
2608.08548 v2

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T04:45:54.121324Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:46:13.302079Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-15T14:46:13.423281Z

Reference resolution

23 of 23 outbound references displayed

  • verified exact1
  • verified fuzzy18
  • unresolved4
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b42ccecf-6466-4ec4-a46a-6238e15224a5 · outbound

This paper cites an unresolved cited work.

An Alexandrov-type theorem in warped product manifolds with radial density Unresolved cited work

Reference 1

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unresolved
raw_fallback, observed 2026-08-14T04:45:54.505798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.012449Z digest=sha256:74f3195857a2208b3c4fbc85478588fa012c16d57a92f47258ab5c07e448eebe

Observation 5d486bcd-2036-4c65-982a-f9f29fe260ba · outbound

This paper cites Some rigidity properties forλ-self-expanders.Nonlinear Anal., 230:113230, 2023.

An Alexandrov-type theorem in warped product manifolds with radial density Some rigidity properties forλ-self-expanders.Nonlinear Anal., 230:113230, 2023

Reference 2

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raw_fallback, observed 2026-08-14T04:45:54.491564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 204a00de-1a64-47fd-b760-05141c49dd5c · outbound

This paper cites The space of asymptotically conical self-expanders of mean curvature flow.Math.

An Alexandrov-type theorem in warped product manifolds with radial density The space of asymptotically conical self-expanders of mean curvature flow.Math

Reference 3

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raw_fallback, observed 2026-08-14T04:45:54.477181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 7792cae5-401c-4932-b8d0-f71124359d1a · outbound

This paper cites The equality case in the substatic Heintze– Karcher inequality.Arch.

An Alexandrov-type theorem in warped product manifolds with radial density The equality case in the substatic Heintze– Karcher inequality.Arch

Reference 4

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raw_fallback, observed 2026-08-14T04:45:54.462791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.028388Z digest=sha256:bb15b2e8b90a162932edad3a8d4589a506b9ad8e585f7d734494fe2577aade72

Observation d11f3ef5-4ece-48e4-a0ec-a30dfaaf8760 · outbound

This paper cites Constant mean curvature surfaces in warped product manifolds.Publ.

An Alexandrov-type theorem in warped product manifolds with radial density Constant mean curvature surfaces in warped product manifolds.Publ

Reference 5

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raw_fallback, observed 2026-08-14T04:45:54.448367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.033477Z digest=sha256:b53418cd1fbb215fd486576534fe5f3b8103745c61ebe987ea7e9d9da7eb009d

Observation c91f76e1-3c90-400d-836f-42a4fa739f75 · outbound

This paper cites Chambers.

An Alexandrov-type theorem in warped product manifolds with radial density Chambers

Reference 6

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.038690Z digest=sha256:50f1b76b1f52d10de91c24873ea00419e2e985c86d1d7024d63a610844df512f

Observation 944a8c95-fd3a-4989-bf66-b43beb6453f3 · outbound

This paper cites Completeλ-hypersurfaces of weighted volume-preserving mean cur- vature flow.Calc.

An Alexandrov-type theorem in warped product manifolds with radial density Completeλ-hypersurfaces of weighted volume-preserving mean cur- vature flow.Calc

Reference 7

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verified fuzzy
raw_fallback, observed 2026-08-14T04:45:54.418795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.044392Z digest=sha256:c48fae9cbbae6a330d7c1009101fefe8018202768ac68ce6f2babde45aac3a73

Observation 5c95116c-c62a-48be-b74f-b123f14467df · outbound

This paper cites Colding and II Minicozzi, William P.

An Alexandrov-type theorem in warped product manifolds with radial density Colding and II Minicozzi, William P

Reference 8

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raw_fallback, observed 2026-08-14T04:45:54.403840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.049337Z digest=sha256:140daa18d1163012934e17ffaa5a99ca43a50af3d486e7eab4fc0d7fd6faf22a

Observation e7b5d20b-4e24-4545-905a-df119b1cdcc0 · outbound

This paper cites Generic uniqueness of expanders with vanishing relative entropy.Math.

An Alexandrov-type theorem in warped product manifolds with radial density Generic uniqueness of expanders with vanishing relative entropy.Math

Reference 9

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raw_fallback, observed 2026-08-14T04:45:54.388354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.053908Z digest=sha256:684008231316dfce5fdbf2ff614d3b26c90c6e21433d569a69e52913cae29843

Observation 3671b47d-c011-412e-b1a0-e0547ae4e225 · outbound

This paper cites Minimal cones and self-expanding solutions for mean curvature flows.Math.

An Alexandrov-type theorem in warped product manifolds with radial density Minimal cones and self-expanding solutions for mean curvature flows.Math

Reference 10

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raw_fallback, observed 2026-08-14T04:45:54.373561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.058562Z digest=sha256:4426ea8bc1192de441049acda13855e473b0e9ca77dd40bb1fe9e9d91d335836

Observation c01ff773-f8fd-4651-a690-c37f49172aa4 · outbound

This paper cites On the isoperimetric problem for radial log-convex densities.Calc.

An Alexandrov-type theorem in warped product manifolds with radial density On the isoperimetric problem for radial log-convex densities.Calc

Reference 11

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raw_fallback, observed 2026-08-14T04:45:54.358758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.063190Z digest=sha256:e29510289233356be4ccef40f6ce0403a20583050699c6a9f470848bada8e9e3

Observation 23c3f2c4-de83-426b-b147-8021e3279f0a · outbound

This paper cites A general comparison theorem with applications to volume estimates for submanifolds.Ann.

An Alexandrov-type theorem in warped product manifolds with radial density A general comparison theorem with applications to volume estimates for submanifolds.Ann

Reference 12

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verified fuzzy
raw_fallback, observed 2026-08-14T04:45:54.342869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.067890Z digest=sha256:beabeca88841b2cb9fd1529d1f8242e8f68a25e866480742afee965e52bc6017

Observation ab31b5f8-a284-432e-a5d9-7fe1a6d6ae02 · outbound

This paper cites Alexandrov’s theorem for anisotropic capillary hypersurfaces in the half-space.Arch.

An Alexandrov-type theorem in warped product manifolds with radial density Alexandrov’s theorem for anisotropic capillary hypersurfaces in the half-space.Arch

Reference 13

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raw_fallback, observed 2026-08-14T04:45:54.325892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.072312Z digest=sha256:e9bbddea03371041332cd6a280735880f3df4fe2150d3eee8abeef64e3344a63

Observation 11f43ab5-972d-47b7-b6fe-015ebd0a6358 · outbound

This paper cites Heintze-Karcher inequality for anisotropic free boundary hypersurfaces in convex domains.J.

An Alexandrov-type theorem in warped product manifolds with radial density Heintze-Karcher inequality for anisotropic free boundary hypersurfaces in convex domains.J

Reference 14

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raw_fallback, observed 2026-08-14T04:45:54.310363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 6b01250b-1d70-403b-a9d6-17077e74c7e6 · outbound

This paper cites Alexandrov Theorem for constant weighted mean curvature surfaces.

An Alexandrov-type theorem in warped product manifolds with radial density Alexandrov Theorem for constant weighted mean curvature surfaces

Reference 15

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local_arxiv, observed 2026-08-14T04:45:54.181431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 88d77ccb-442f-4c58-83ce-3280e3645b45 · outbound

This paper cites an unresolved cited work.

An Alexandrov-type theorem in warped product manifolds with radial density Unresolved cited work

Reference 16

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.086870Z digest=sha256:a4e2bf11233f2f985e59db37f2c01fb3226c26eb405b61152545744acd91dba9

Observation 90684afa-b160-4b9e-9054-3d3c9638ba98 · outbound

This paper cites New Heintze-Karcher type inequalities in sub-static warped product manifolds.

An Alexandrov-type theorem in warped product manifolds with radial density New Heintze-Karcher type inequalities in sub-static warped product manifolds

Reference 17

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no resolver link, observed 2026-08-14T04:45:54.091609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T04:45:54.091609Z digest=sha256:0d229ad87a9cea19ff95ccd5effc6e0424563ff403345aa9342861f2d391c7ac

Observation 81e6ab8d-ea98-4deb-9a7f-2dc633edf33e · outbound

This paper cites An integral formula and its applications on sub-static manifolds.J.

An Alexandrov-type theorem in warped product manifolds with radial density An integral formula and its applications on sub-static manifolds.J

Reference 18

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verified fuzzy
raw_fallback, observed 2026-08-14T04:45:54.279236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 5d0604fa-83c0-48e3-a95b-5cfe36703d54 · outbound

This paper cites Manifolds with density.Notices Amer.

An Alexandrov-type theorem in warped product manifolds with radial density Manifolds with density.Notices Amer

Reference 19

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verified fuzzy
raw_fallback, observed 2026-08-14T04:45:54.262132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.102130Z digest=sha256:58b00065c3e4377fef083591f158706a5af25c709af3d3eb513892de19ee6ca4

Observation 360f4ef1-cb55-4bd2-ab75-e18b39042878 · outbound

This paper cites an unresolved cited work.

An Alexandrov-type theorem in warped product manifolds with radial density Unresolved cited work

Reference 20

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raw_fallback, observed 2026-08-14T04:45:54.246492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.107220Z digest=sha256:78b7c2c7971c4657805fc0ce485abf5a6e296413600516579f1c8b8be567bf0e

Observation 84e67218-ea4d-4b95-b9b4-96bc429236e1 · outbound

This paper cites Compact hypersurfaces with constant higher order mean curvatures.Rev.

An Alexandrov-type theorem in warped product manifolds with radial density Compact hypersurfaces with constant higher order mean curvatures.Rev

Reference 21

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verified fuzzy
raw_fallback, observed 2026-08-14T04:45:54.230349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.111825Z digest=sha256:d3bc891173cf8366ea3916f934b218edead3fcc07677658c0379dcbf0349dd3f

Observation cb4878ec-4984-474e-a00c-993409f9206c · outbound

This paper cites Rosales, A.

An Alexandrov-type theorem in warped product manifolds with radial density Rosales, A

Reference 22

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raw_fallback, observed 2026-08-14T04:45:54.214517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.116589Z digest=sha256:8c17c430171ad907581cdcaf88cad26703077e52719d8fe105e67341243e01e7

Observation 329c068b-0636-4050-b785-31cc68a36679 · outbound

This paper cites Capillary hypersurfaces, Heintze-Karcher’s inequality and Zermelo’s navi- gation.Calc.

An Alexandrov-type theorem in warped product manifolds with radial density Capillary hypersurfaces, Heintze-Karcher’s inequality and Zermelo’s navi- gation.Calc

Reference 23

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verified fuzzy
raw_fallback, observed 2026-08-14T04:45:54.198153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T04:45:54.121324Z digest=sha256:a9e597f6630eb179699f6f642698e0f8bf1662dc2700cb7226933ed62bf77676

Pith citing papers

Observation 5c8ed967-315c-44ae-89c5-05d21d6c2abd · inbound

Alexandrov Theorem for constant weighted mean curvature surfaces cites this paper.

Alexandrov Theorem for constant weighted mean curvature surfaces An Alexandrov-type theorem in warped product manifolds with radial density

Reference 3

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local_arxiv, observed 2026-08-15T14:46:13.428767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T14:46:13.302079Z digest=sha256:5e48252d5cc70d918a3361e9ec8eca80e94ea626ad4aa725206e03566a7c3b38