Paper Citation Record · LEDGER

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime

As of 14 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 4 inbound Pith citation observations for arXiv:2412.01012.

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pith.paper-citation-record.v1
2412.01012 v2

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measured 29 of 29 reference resolution

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Source: arxiv_reference, observed 2026-07-04T12:19:49.210293Z

Reference resolution

29 of 29 outbound references displayed

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Outbound references

Observation 9954b59a-87bb-44b8-92ec-f5c99d6ead82 · outbound

This paper cites A user’s guide to optimal transport.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime A user’s guide to optimal transport

Reference 1

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Observation a73735d8-23cf-4d06-9933-b0753de0c6e8 · outbound

This paper cites Lectures in Mathematics ETH Z¨urich.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Lectures in Mathematics ETH Z¨urich

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.722187Z

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Observation 2949587b-42b0-4993-a50e-f8182040c130 · outbound

This paper cites Existence and stability results in theL 1 theory of optimal transportation.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Existence and stability results in theL 1 theory of optimal transportation

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.705960Z

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Observation 5d0b0c4d-7756-4cad-86cf-95b73ae9210d · outbound

This paper cites Routledge, London, England, 2017.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Routledge, London, England, 2017

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.689204Z

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Observation 3423ed8e-b8f6-453c-8706-e5a76e73c5b1 · outbound

This paper cites Globally hyperbolic spacetimes can be defined as ‘causal’ instead of ‘strongly causal’.Class.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Globally hyperbolic spacetimes can be defined as ‘causal’ instead of ‘strongly causal’.Class

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.673995Z

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Observation 340c86b0-5160-4deb-8cd0-5aafcdbc8a0f · outbound

This paper cites Lyapounov functions of closed cone fields: from Conley theory to time functions.Comm.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Lyapounov functions of closed cone fields: from Conley theory to time functions.Comm

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.658626Z

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Observation 76fe6666-8f28-4ecb-bff2-49a3794d87d4 · outbound

This paper cites Kantorovich potentials and continuity of total cost for relativistic cost functions.Journal de Math´ ematiques Pures et Appliqu´ ees, 110:93–122, 2018.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Kantorovich potentials and continuity of total cost for relativistic cost functions.Journal de Math´ ematiques Pures et Appliqu´ ees, 110:93–122, 2018

Reference 7

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Observation eecf63f1-a648-4a4c-8534-fc95b7be6a31 · outbound

This paper cites The optimal mass transport problem for relativistic costs.Calculus of Variations and Partial Differential Equations, 46:353 – 374, 2012.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime The optimal mass transport problem for relativistic costs.Calculus of Variations and Partial Differential Equations, 46:353 – 374, 2012

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.626629Z

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Observation 447dbd88-c23a-49e7-9c1c-d3bf1970a146 · outbound

This paper cites Polar factorization and monotone rearrangement of vector-valued functions.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Polar factorization and monotone rearrangement of vector-valued functions

Reference 9

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Observation 0be4674f-6239-4b1b-a9fd-cd86ea22afd5 · outbound

This paper cites Extended Monge-Kantorovich theory.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Extended Monge-Kantorovich theory

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.601396Z

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Observation 379e26a8-ca2e-43fa-8b55-88b64fd17cf7 · outbound

This paper cites Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications.Camb.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications.Camb

Reference 11

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Observation 19998e09-938b-4901-80fd-b705f40c93f7 · outbound

This paper cites Causality for nonlocal phenomena.Ann.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Causality for nonlocal phenomena.Ann

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-12T04:52:58.201339Z

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Observation eae5e0c7-284f-4304-815e-113e308121db · outbound

This paper cites Optimal transportation on non-compact manifolds.Israel J.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Optimal transportation on non-compact manifolds.Israel J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.565374Z

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Observation ebcc60f3-74e8-4a40-91b7-a0783f2f74a9 · outbound

This paper cites Local semiconvexity of Kantorovich potentials on non- compact manifolds.ESAIM Control Optim.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Local semiconvexity of Kantorovich potentials on non- compact manifolds.ESAIM Control Optim

Reference 14

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Observation 4cb58238-5aaf-48f2-8ea1-4935b1f1085a · outbound

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Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Unresolved cited work

Reference 15

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Observation cc420813-9ba4-4cc0-ae1e-0f4154d02475 · outbound

This paper cites Kantorovitch.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Kantorovitch

Reference 16

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Observation 91e05020-fc90-43e1-9319-75d6497e217d · outbound

This paper cites On the existence of dual solutions for Lorentzian cost func- tions.Ann.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime On the existence of dual solutions for Lorentzian cost func- tions.Ann

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.502280Z

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Observation bc3df2ef-bf0e-436f-a259-8ca9e0c3e5f1 · outbound

This paper cites Ricci curvature for metric-measure spaces via optimal trans- port.Ann.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Ricci curvature for metric-measure spaces via optimal trans- port.Ann

Reference 18

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Observation b040d8b7-1461-4d3d-8527-0eb7e88e4b66 · outbound

This paper cites On the continuity of the total cost in the mass transport problem with relativistic cost functions, 2016.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime On the continuity of the total cost in the mass transport problem with relativistic cost functions, 2016

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.470463Z

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Observation bf11b400-01f4-40dd-9add-c3216ce5269e · outbound

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Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Unresolved cited work

Reference 20

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Observation 4f7ecc3c-eb71-4dff-9e05-a71104c36721 · outbound

This paper cites an unresolved cited work.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-12T04:52:58.241929Z

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Observation e142658f-e901-45b5-9c90-730e58fcf3ee · outbound

This paper cites Lorentzian causality theory.Living Reviews in Relativity, 22:1–202, 2019.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Lorentzian causality theory.Living Reviews in Relativity, 22:1–202, 2019

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.428589Z

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Observation bcad7fac-e91e-4ad2-80f3-303bba98ce61 · outbound

This paper cites An optimal transport formulation of the Einstein equa- tions of general relativity.J.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime An optimal transport formulation of the Einstein equa- tions of general relativity.J

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.412805Z

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Observation b2c7d946-72ad-44ca-9abf-fc3220ec8fdb · outbound

This paper cites Monge.M´ emoire sur la th´ eorie des d´ eblais et des remblais.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Monge.M´ emoire sur la th´ eorie des d´ eblais et des remblais

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.395725Z

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Observation ad74ea6f-fd39-4917-8c7b-750b2f217b4e · outbound

This paper cites Academic Press, San Diego, CA, USA, 1983.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Academic Press, San Diego, CA, USA, 1983

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.379255Z

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Observation 9958ca94-f6ba-4230-9c4a-cc5656ad1af7 · outbound

This paper cites On the geometry of metric measure spaces.Acta Mathematica, 196(1):65 – 131, 2006.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime On the geometry of metric measure spaces.Acta Mathematica, 196(1):65 – 131, 2006

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.363713Z

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Observation 32c5e973-1e1d-4109-a6da-3547ce2a0ed3 · outbound

This paper cites On the geometry of metric measure spaces.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime On the geometry of metric measure spaces

Reference 27

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Observation 7db15c8c-948d-41d7-888e-a935e5e161c4 · outbound

This paper cites Theory of optimal transport for Lorentzian cost functions.M ¨unster J.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Theory of optimal transport for Lorentzian cost functions.M ¨unster J

Reference 28

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Observation 58c3d767-b4a1-450f-81d8-13edee936456 · outbound

This paper cites Springer, Berlin, 2009 edition, 2008.

Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime Springer, Berlin, 2009 edition, 2008

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:52:58.315462Z

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Pith citing papers

Observation cdc02502-d1f1-47f5-8d00-d8ad1ccc32d6 · inbound

On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime cites this paper.

On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime

Reference 17

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Observation a1236a33-edc6-4b8e-b526-743db432d208 · inbound

Semiconvexity of (weak) Kantorovich potentials in the Lorentzian optimal transport problem cites this paper.

Semiconvexity of (weak) Kantorovich potentials in the Lorentzian optimal transport problem Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime

Reference 23

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Observation 2845ac19-f677-4c36-9fc2-83c444df079c · inbound

A Lorentzian Lasry-Lions regularization theorem cites this paper.

A Lorentzian Lasry-Lions regularization theorem Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime

Reference 17

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Observation 99d996b9-e6df-4cd4-b123-d0679177c873 · inbound

Lipschitz continuity of the cut time for globally hyperbolic spacetimes cites this paper.

Lipschitz continuity of the cut time for globally hyperbolic spacetimes Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime

Reference 34

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