Paper Citation Record · LEDGER

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces

As of 23 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 3 inbound Pith citation observations for arXiv:1909.00381.

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

pith.paper-citation-record.v1
1909.00381 v1

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T06:05:22.762984Z

measured 51 of 51 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-30T14:11:19.315088Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-30T12:54:39.742803Z

Reference resolution

48 of 48 outbound references displayed

verified exact10
verified fuzzy22
unresolved16
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External citation measurements

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Outbound references

Observation 256a6d96-41be-4c2d-b299-27624f3cd9e8 · outbound

This paper cites Ambrosio , Fine properties of sets of ﬁnite perimeter in doubling metri c measure spaces, Set-Valued Anal., 10 (2002), pp.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Ambrosio , Fine properties of sets of ﬁnite perimeter in doubling metri c measure spaces, Set-Valued Anal., 10 (2002), pp

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.318893Z

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Observation e6b34468-4dc7-4e43-be17-d17a409d9812 · outbound

This paper cites Rigidity of the 1-Bakry-\'Emery inequality and sets of finite perimeter in RCD spaces.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Rigidity of the 1-Bakry-\'Emery inequality and sets of finite perimeter in RCD spaces

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.591976Z

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Observation 4dfd8147-5efd-4041-b604-22d90644cc4d · outbound

This paper cites Ambrosio and S.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Ambrosio and S

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.306496Z

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Observation 836850f6-5b02-49ec-b4d5-b48daf8a4584 · outbound

This paper cites Ambrosio, N.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Ambrosio, N

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.601616Z

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Observation 27628e68-5e90-4438-a383-684959e43125 · outbound

This paper cites Ambrosio, N.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Ambrosio, N

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.289981Z

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Observation d264f415-a992-4873-a084-8838add9262e · outbound

This paper cites Ambrosio and S.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Ambrosio and S

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.279841Z

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Observation 0a794ce4-131b-44da-a2a6-835e7c64c6c7 · outbound

This paper cites an unresolved cited work.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-14T06:05:23.269458Z

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Observation c6b695a3-5eef-4148-81d2-96f3fb05c2dc · outbound

This paper cites Embedding of $RCD^*(K,N)$ spaces in $L^2$ via eigenfunctions.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Embedding of $RCD^*(K,N)$ spaces in $L^2$ via eigenfunctions

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-14T06:05:22.975202Z

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Observation 8d87d6d9-0144-4c42-a324-561cae0c3256 · outbound

This paper cites Nonlinear diffusion equations and curvature conditions in metric measure spaces.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Nonlinear diffusion equations and curvature conditions in metric measure spaces

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.621759Z

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Observation ab372d85-d613-4b16-bbec-0e0953d01ee0 · outbound

This paper cites Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-14T06:05:22.950540Z

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Observation f244088f-174a-4d07-9d87-08f62825f074 · outbound

This paper cites Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-14T06:05:22.935317Z

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Observation 7be6f825-9f6b-4494-8ddb-64fdfe0b9ca5 · outbound

This paper cites On $BV$ functions and essentially bounded divergence-measure fields in metric spaces.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces On $BV$ functions and essentially bounded divergence-measure fields in metric spaces

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-14T06:05:22.920720Z

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Observation a978f556-721b-43c1-82d3-1e908e4b1d2e · outbound

This paper cites The Globalization Theorem for the Curvature Dimension Condition.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces The Globalization Theorem for the Curvature Dimension Condition

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-14T06:05:22.904656Z

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Observation 4a7e7ef2-1e29-412e-83b5-447a3967fe69 · outbound

This paper cites Cheeger and T.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Cheeger and T

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.257605Z

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Observation cac45403-948b-4b31-be84-1ec1fa6d58fa · outbound

This paper cites an unresolved cited work.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Unresolved cited work

Reference 17

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Observation d46d93fc-987d-4e4b-bdd7-a9c0d33771be · outbound

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Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-14T06:05:23.240668Z

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Observation 49ca960a-69bb-4a1d-96a0-b9c7a113f0a7 · outbound

This paper cites Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-14T06:05:22.889821Z

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Observation 5f596135-f77d-4126-8ad4-c43565297305 · outbound

This paper cites Cheeger and A.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Cheeger and A

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.229256Z

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Observation 14a9600c-ad01-46c6-b9d9-62ae8a0f8088 · outbound

This paper cites De Philippis, A.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces De Philippis, A

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.218086Z

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Observation 3351b6e0-a342-4760-aa9f-e1cfe8abe61f · outbound

This paper cites Quasi-continuous vector fields on RCD spaces.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Quasi-continuous vector fields on RCD spaces

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-14T06:05:22.874667Z

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Observation 9139296d-420d-4346-8f7b-4ce55f7ff615 · outbound

This paper cites Sobolev and BV spaces on metric measure spaces via derivations and integration by parts.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Sobolev and BV spaces on metric measure spaces via derivations and integration by parts

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.667127Z

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Observation d61260b5-c686-4620-a057-bdda92bc8124 · outbound

This paper cites Infinitesimal Hilbertianity of locally CAT($\kappa$)-spaces.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Infinitesimal Hilbertianity of locally CAT($\kappa$)-spaces

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-14T06:05:22.849760Z

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Observation 0895011b-dbda-403c-913f-fd1a80e26c33 · outbound

This paper cites Erbar, K.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Erbar, K

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.207464Z

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Observation b75fb15d-3609-4de3-8916-5811a75d6809 · outbound

This paper cites Evans and R.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Evans and R

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.197554Z

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Observation 1fe9c6d8-96f3-447f-87d5-8fdeb293b507 · outbound

This paper cites Gigli , Nonsmooth diﬀerential geometry - an approach tailored for s paces with Ricci curvature bounded from below.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Gigli , Nonsmooth diﬀerential geometry - an approach tailored for s paces with Ricci curvature bounded from below

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.186840Z

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Observation 68dae988-2e0d-416b-9854-947f848bbc45 · outbound

This paper cites an unresolved cited work.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.684699Z

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Observation 3042f043-3d22-40b4-9348-92a17bd62ee3 · outbound

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Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-14T06:05:23.167714Z

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Observation 74b7d330-47c0-46b4-b66d-5afc12bf9c47 · outbound

This paper cites Gigli and B.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Gigli and B

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.691533Z

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Observation e6b38de6-e757-4b1f-8380-f37840f273df · outbound

This paper cites Gigli, A.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Gigli, A

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.150563Z

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Observation 8eff57df-1d74-45bc-8c12-c054d02e2890 · outbound

This paper cites Gigli and E.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Gigli and E

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.140880Z

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Observation 042a3669-a4f1-4e55-9313-65049142d38b · outbound

This paper cites Accepted at Communications in Analysis and Geometry, arXiv:1611.09 645.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Accepted at Communications in Analysis and Geometry, arXiv:1611.09 645

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.129699Z

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Observation 3820ca49-b841-4fe8-8486-70034f46b009 · outbound

This paper cites Ricci tensor on ${\rm RCD}^*(K,N)$ spaces.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Ricci tensor on ${\rm RCD}^*(K,N)$ spaces

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-08-14T06:05:22.834834Z

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Observation b44a34fd-e487-4a94-886a-f8e632285530 · outbound

This paper cites Jiang , Cheeger-harmonic functions in metric measure spaces revis ited, J.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Jiang , Cheeger-harmonic functions in metric measure spaces revis ited, J

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.120119Z

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Observation abcc6684-172e-4066-a6de-bae6ad687b83 · outbound

This paper cites Metric-measure boundary and geodesic flow on Alexandrov spaces.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Metric-measure boundary and geodesic flow on Alexandrov spaces

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-14T06:05:22.819999Z

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Observation 947ae89d-0f39-4713-a2ee-4765cc741ba3 · outbound

This paper cites On the topology and the boundary of N-dimensional RCD(K,N) spaces.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces On the topology and the boundary of N-dimensional RCD(K,N) spaces

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.716733Z

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Observation 07a8dc8b-1b38-45fb-bfde-b84c87c9c647 · outbound

This paper cites Kell and A.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Kell and A

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.110419Z

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Observation f0b40cb7-4e76-414c-85df-a0b8d0c8ec0d · outbound

This paper cites Lott and C.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Lott and C

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.723996Z

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Observation f798d33d-8131-4bab-9f40-b316380c7a60 · outbound

This paper cites Magnani, On a measure theoretic area formula , Proc.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Magnani, On a measure theoretic area formula , Proc

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.092757Z

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Observation 4eba4d64-2648-452c-b4ce-7e974df8c203 · outbound

This paper cites Miranda, Jr.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Miranda, Jr

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.081152Z

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Observation 45d79f7a-2e04-4db0-9e77-af236f0ca76a · outbound

This paper cites Structure Theory of Metric-Measure Spaces with Lower Ricci Curvature Bounds.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Structure Theory of Metric-Measure Spaces with Lower Ricci Curvature Bounds

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.734578Z

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Unavailable: canonical work link unavailable.

Observation a0b9478a-59f1-47de-a88e-e3dcba6e9ec4 · outbound

This paper cites Petrunin , Alexandrov meets Lott-Villani-Sturm , M¨ unster J.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Petrunin , Alexandrov meets Lott-Villani-Sturm , M¨ unster J

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.068629Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 07f0bc9d-cbbd-49cc-a109-a271429ab4b9 · outbound

This paper cites an unresolved cited work.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-14T06:05:23.056843Z

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Observation b7a53c5e-278f-4b64-9d76-80a9b5c987b4 · outbound

This paper cites Rajala , Local Poincar´ e inequalities from stable curvature conditions on metric spaces , Calc.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Rajala , Local Poincar´ e inequalities from stable curvature conditions on metric spaces , Calc

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.047108Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation dbf0218b-4f67-4cf4-a22f-8e136543a7e3 · outbound

This paper cites Savar´e, Self-improvement of the Bakry- ´Emery condition and Wasserstein contraction of the heat ﬂow in RCD(K, ∞ ) metric measure spaces , Discrete Contin.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Savar´e, Self-improvement of the Bakry- ´Emery condition and Wasserstein contraction of the heat ﬂow in RCD(K, ∞ ) metric measure spaces , Discrete Contin

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.035489Z

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Observation 5f462f59-f224-4fd1-b6e0-f860f8339146 · outbound

This paper cites Sturm , On the geometry of metric measure spaces.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Sturm , On the geometry of metric measure spaces

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.752624Z

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Observation e3fc3a5a-f746-4b88-a7d8-66ff452b7ca3 · outbound

This paper cites II , Acta Math., 196 (2006), pp.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces II , Acta Math., 196 (2006), pp

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-14T06:05:22.756096Z

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Observation 14a70177-2035-4acb-a4ad-334a1c2eec6d · outbound

This paper cites Villani , Optimal transport.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Villani , Optimal transport

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:23.009438Z

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Observation cb74d7e1-daaa-440e-bb5f-7125bea603b3 · outbound

This paper cites Weaver , Lipschitz algebras and derivations.

Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces Weaver , Lipschitz algebras and derivations

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:05:22.998076Z

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Pith citing papers

Observation 0f8ba49a-3c95-4a2a-9d2b-58432e57d37f · inbound

One-phase Free Boundary Problems on RCD Metric Measure Spaces cites this paper.

One-phase Free Boundary Problems on RCD Metric Measure Spaces Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-24T12:49:29.589126Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9ba675b5-39af-4cd0-9b7c-36a046c6e2f2 · inbound

Fibrations, the First Betti Number, and Almost Nonnegative Ricci Curvature cites this paper.

Fibrations, the First Betti Number, and Almost Nonnegative Ricci Curvature Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces

Reference 14

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Lipschitz continuity of harmonic maps between ${\rm RCD}(K,N)$ spaces and ${\rm CAT}(\kappa)$ spaces cites this paper.

Lipschitz continuity of harmonic maps between ${\rm RCD}(K,N)$ spaces and ${\rm CAT}(\kappa)$ spaces Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces

Reference 128

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