Regularity of optimal transport in curved geometry: The nonfocal case

By Grégoire Loeper, Cédric Villani. 2010

89 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/161530555314b91bf610c3a73d3fd20ae5265cc8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

Citations in the corpus

Hölder Continuity and Injectivity of Optimal Maps (2011, background): “Other proofs and extensions appear in [52] [50] [54] [44] [21]: Theorem 3.”
The Monge–Ampère equation and its link to optimal transportation (2013, background): “hus, the above description of the cut-locus in terms of the squared distance can be informally summarized as follows: (4.16) y2cut(x) , D yyd2(x;y)vv= 1 for some v2T yM: Based on this observation, in [89] Loeper and Villani noticed the existence of a deep connection between the MTW condition and the”
Nearly Round Spheres Look Convex (2012, methodology): “It is extracted from [14]; precursors appeared in [22, 28].”
STABILITY OF A 4TH-ORDER CURVATURE CONDITION ARISING IN OPTIMAL TRANSPORT THEORY (2008, methodology): “In the last part of this paper, I shall consider the converse stability problem (stability under perturbation rather than under limit): what can be said, in terms of regularity of optimal transport, of a perturbation of a manifold satisfying the above-mentioned fourth-order condition? This work is a”
Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊2 (2009, background): “…in the case of the flat torus or nearly flat metrics [8, 10], on the standard sphere and its perturbations [11, 17, 19], and on manifolds with nonfocal cut locus [20] (see [28, Chapter 12] for an introduction to the problem of the regularity of the optimal tranport map for a general cost function).”
On the Ma–Trudinger–Wang curvature on surfaces (2010, methodology): “Examples of regular manifolds appear in [10, 11, 23, 24, 19].”