STABILITY OF A 4TH-ORDER CURVATURE CONDITION ARISING IN OPTIMAL TRANSPORT THEORY
By Cédric Villani. 2008
46 citations recorded by the source corpus.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7f8a8656010afe1dcc7cad5c6466ed190773b33e
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In Applied Mathematics
- Alessio Figalli
- Cédric Villani
- Robert J. McCann
- Young-Heon Kim
- Ludovic Rifford
- Grégoire Loeper
- Guido De Philippis
- Filippo Santambrogio
In Geometry and Topology
- Alessio Figalli
- Cédric Villani
- Young-Heon Kim
- Robert J. McCann
- Ludovic Rifford
- Grégoire Loeper
- Guido De Philippis
- Filippo Santambrogio
Citations in the corpus
- Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊2 (2009, background): “Thus, by McCann’s Theorem, the optimal transport map T from µ to ν exists and is unique.”
- Regularity of optimal transport in curved geometry: The nonfocal case (2010, background): “For instance, it is adapted in [31] to prove the stability of the Hölder continuity at a given “mesoscopic” scale under C(2) (not C(4)) perturbations of the metric.”
- NECESSARY AND SUFFICIENT CONDITIONS FOR CONTINUITY OF OPTIMAL TRANSPORT MAPS ON RIEMANNIAN MANIFOLDS (2011, result): “1, we deduce that the set of two-dimensional manifolds satisfying (TCP) is closed in C2-topology (compare with the stability results in [32]).”
- Nearly Round Spheres Look Convex (2012, methodology): “1 is natural and simple, our proof is quite indirect, since it is based on the Ma-Trudinger-Wang curvature tensor (MTW tensor), introduced in [29] and further studied in [9, 14, 15, 23, 22, 26, 28, 33, 34], in relation with the regularity theory of optimal transport; see [13] or [34, Chapter 12] for”
- On the Ma–Trudinger–Wang curvature on surfaces (2010, background): “otherwise we could pass to the limit (as in [29]) to deduce the same property for the limit M .”
- Continuity, curvature, and the general covariance of optimal transportation (2007, background): “It is a pleasure to thank Neil Trudinger, Xu-Jia Wang, Gregoire Loeper, and Cedric Villani for many fruitful discussions, and for providing us with preprints of their inspiring works.”