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Continuity, curvature, and the general covariance of optimal transportation

https://doi.org/10.4171/jems/221
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/cpa.3160450905openalex-snapshot
Boundary regularity of maps with convex potentials
inferredcites →https://doi.org/10.1007/978-3-540-71050-9openalex-snapshot
Optimal Transport: Old and New
inferredcites →https://doi.org/10.1007/978-3-7643-8722-8openalex-snapshot
Gradient Flows: In Metric Spaces and in the Space of Probability Measures
inferredcites →https://doi.org/10.1007/978-4-431-53979-7_1openalex-snapshot
Duality and existence for a class of mass transportation problems and economic applications
inferredcites →https://doi.org/10.1007/b98893openalex-snapshot
Mass Transportation Problems
inferredcites →https://doi.org/10.1007/bf02392620openalex-snapshot
The geometry of optimal transportation
inferredcites →https://doi.org/10.1007/pl00001679openalex-snapshot
Polar factorization of maps on Riemannian manifolds
inferredcites →https://doi.org/10.1007/s00199-009-0455-zopenalex-snapshot
Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness
inferredcites →https://doi.org/10.1007/s00205-005-0362-9openalex-snapshot
Regularity of Potential Functions of the Optimal Transportation Problem
inferredcites →https://doi.org/10.1007/s00205-008-0147-zopenalex-snapshot
On Strict Convexity and Continuous Differentiability of Potential Functions in Optimal Transportation
inferredcites →https://doi.org/10.1007/s00526-003-0239-4openalex-snapshot
On the design of a reflector antenna II
inferredcites →https://doi.org/10.1007/s00526-006-0006-4openalex-snapshot
Gradient estimates for potentials of invertible gradient–mappings on the sphere
inferredcites →https://doi.org/10.1007/s10958-006-0049-2openalex-snapshot
On the Translocation of Masses
inferredcites →https://doi.org/10.1007/s11511-009-0037-8openalex-snapshot
On the regularity of solutions of optimal transportation problems
inferredcites →https://doi.org/10.1016/j.difgeo.2003.10.003openalex-snapshot
Gradient rearrangement for diffeomorphisms of a compact manifold
inferredcites →https://doi.org/10.1016/j.jfa.2008.07.003openalex-snapshot
Stability of a 4th-order curvature condition arising in optimal transport theory
inferredcites →https://doi.org/10.1016/s0294-1449(16)30256-6openalex-snapshot
Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator
inferredcites →https://doi.org/10.1016/s0764-4442(00)88593-6openalex-snapshot
Sur le transport de mesures périodiques
inferredcites →https://doi.org/10.1023/a:1024856201493openalex-snapshot
Optical Design of Single Reflector Systems and the Monge–Kantorovich Mass Transfer Problem
inferredcites →https://doi.org/10.1088/0266-5611/12/3/013openalex-snapshot
On the design of a reflector antenna
inferredcites →https://doi.org/10.1090/conm/353/06432openalex-snapshot
Non-smooth differential properties of optimal transport
inferredcites →https://doi.org/10.1090/gsm/058openalex-snapshot
Topics in Optimal Transportation
inferredcites →https://doi.org/10.1090/qam/1788425openalex-snapshot
Shape recognition via Wasserstein distance
inferredcites →https://doi.org/10.1090/s0002-9947-00-02548-4openalex-snapshot
Conformally invariant Monge-Ampère equations: Global solutions
inferredcites →https://doi.org/10.1090/s0894-0347-1992-1124980-8openalex-snapshot
The Regularity of Mappings with a Convex Potential
inferredcites →https://doi.org/10.1093/imrn/rnn120openalex-snapshot
Counterexamples to Continuity of Optimal Transport Maps on Positively Curved Riemannian Manifolds
inferredcites →https://doi.org/10.1112/blms/16.3.328openalex-snapshot
SEMI-RIEMANNIAN GEOMETRY With Applications to Relativity
inferredcites →https://doi.org/10.1142/9789812772688_0018openalex-snapshot
CONFORMAL GEOMETRY AND FULLY NONLINEAR EQUATIONS
inferredcites →https://doi.org/10.1201/9780203744369-4openalex-snapshot
Allocation Maps with General Cost Functions
inferredcites →https://doi.org/10.1215/00127094-2010-003openalex-snapshot
Regularity of optimal transport in curved geometry: The nonfocal case
inferredcites →https://doi.org/10.1215/s0012-7094-00-10127-5openalex-snapshot
Conformal geometry, contact geometry, and the calculus of variations
inferredcites →https://doi.org/10.1215/s0012-7094-95-08013-2openalex-snapshot
Existence and uniqueness of monotone measure-preserving maps
inferredcites →https://doi.org/10.1515/crelle.2011.105openalex-snapshot
Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular)
inferredcites →https://doi.org/10.1515/crll.1997.487.115openalex-snapshot
On the second boundary value problem for equations of Monge-Ampère type.
inferredcites →https://doi.org/10.2307/2118564openalex-snapshot
Boundary Regularity of Maps with Convex Potentials--II
inferredcites →https://doi.org/10.4007/annals.2008.167.299openalex-snapshot
On the regularity of reflector antennas
inferredcites →https://doi.org/10.4171/022-3/15openalex-snapshot
Recent developments in elliptic partial differential equations of Monge–Ampère type
inferredcites →https://doi.org/10.4171/jems/221openalex-snapshot
Continuity, curvature, and the general covariance of optimal transportation
inferredcites →https://doi.org/10.4310/jdg/1214459935openalex-snapshot
Minimal Lagrangian diffeomorphisms and the Monge-Ampère equation
inferredcites →https://doi.org/10.4310/maa.2008.v15.n2.a3openalex-snapshot
An Approximation Lemma about the Cut Locus, with Applications in Optimal Transport Theory
inferredcites →https://doi.org/10.48550/arxiv.0706.1226openalex-snapshot
On the cost-subdifferentials of cost-convex functions
inferredcites →https://doi.org/10.48550/arxiv.0709.1653openalex-snapshot
Counterexamples to continuity of optimal transportation on positively curved Riemannian manifolds
inferredcites →https://doi.org/10.48550/arxiv.0911.3952openalex-snapshot
Continuity and injectivity of optimal maps for non-negatively cross-curved costs
inferredcites →https://doi.org/10.48550/arxiv.math/0504137openalex-snapshot
On the regularity of maps solutions of optimal transportation problems
inferredcites →https://doi.org/10.48550/arxiv.math/0702807openalex-snapshot
On strict convexity and $C^1$ regularity of potential functions in optimal transportation

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Geometry in Global Coordinates with Applications in Mechanics and Optimal Transport
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On Asymptotic Behaviour and W 2, p Regularity of Potentials in Optimal Transportation
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Hölder regularity of optimal mappings in optimal transportation
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C 1 regularity of solutions of the Monge–Ampère equation for optimal transport in dimension two
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Example of a displacement convex functional of first order
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An iterative scheme for solving the optimal transportation problem
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Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces
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On the local geometry of maps with c-convex potentials
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Continuity and injectivity of optimal maps
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Strict convexity and $$C^1$$ regularity of solutions to generated Jacobian equations in dimension two
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First and second derivative Hölder estimates for generated Jacobian equations
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Metric extrapolation in the Wasserstein space
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On the Regularity of Optimal Transportation Potentials on Round Spheres
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Invariant Monge–Ampère equations on contactified para–Kähler manifolds
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Polar factorization of conformal and projective maps of the sphere in the sense of optimal mass transport
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Variational Approach to Regularity of Optimal Transport Maps: General Cost Functions
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Pseudo-Riemannian geometry encodes information geometry in optimal transport
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When optimal transport meets information geometry
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Conformal mirror descent with logarithmic divergences
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Families of costs with zero and nonnegative MTW tensor in optimal transport and the c-divergences
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Boundary ε-regularity in optimal transportation
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Wasserstein barycenters over Riemannian manifolds
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Convexity and multi-dimensional screening for spaces with different dimensions
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Locally nearly spherical surfaces are almost-positively $c$-curved
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Pseudo-Riemannian geometry calibrates optimal transportation
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Regularity of optimal transportation between spaces with different dimensions
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Counterexamples to continuity of optimal transportation on positively curved Riemannian manifolds
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Optimal Transport and Tessellation
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The Ma-Trudinger-Wang curvature for natural mechanical actions
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Continuity and injectivity of optimal maps for non-negatively cross-curved costs
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New examples on spaces of negative sectional curvature satisfying Ma-Trudinger-Wang conditions
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Extremal doubly stochastic measures and optimal transportation
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Regularity of optimal transport maps on multiple products of spheres
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Locally nearly spherical surfaces are almost-positively $c$-curved
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An iterative scheme for solving the optimal transportation problem
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Sobolev regularity for Monge-Ampère type equations
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On the local theory of prescribed Jacobian equations
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The local geometry of maps with c-convex potentials
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The Monge-Ampère equation and its link to optimal transportation
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On the convexity of injectivity domains on nonfocal manifolds
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Boundary $\varepsilon$-regularity in optimal transportation
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Partial $W^{2,p}$ regularity for optimal transport maps
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Semi-Riemannian Manifold Optimization
inferred← citeshttps://doi.org/10.48550/arxiv.1906.00030openalex-snapshot
Pseudo-Riemannian geometry embeds information geometry in optimal transport
inferred← citeshttps://doi.org/10.48550/arxiv.1911.04348openalex-snapshot
Semi-discrete optimal transport
inferred← citeshttps://doi.org/10.48550/arxiv.2010.14471openalex-snapshot
Synthetic MTW conditions and their equivalence under mild regularity assumption on the cost function
inferred← citeshttps://doi.org/10.48550/arxiv.2112.11056openalex-snapshot
Regularity theory and geometry of unbalanced optimal transport
inferred← citeshttps://doi.org/10.5802/afst.1678openalex-snapshot
Regularity of optimal transport maps on locally nearly spherical manifolds
inferred← citeshttps://doi.org/10.70675/92863850zf500z4057z83b5z7944554e7a71openalex-snapshot
Regularity of optimal transport map on compact Riemannian manifolds
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