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On the convexity of injectivity domains on nonfocal manifolds

Alessio Figalli 1 Thomas Gallouët 2 Ludovic Rifford 3, 4 
2 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe, ULB - Université libre de Bruxelles
3 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Given a smooth nonfocal compact Riemannian manifold, we show that the so-called Ma--Trudinger--Wang condition implies the convexity of injectivity domains. This improves a previous result by Loeper and Villani.
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https://hal.inria.fr/hal-00968354
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Submitted on : Monday, March 31, 2014 - 7:27:24 PM
Last modification on : Tuesday, November 22, 2022 - 2:26:15 PM
Long-term archiving on: : Monday, April 10, 2017 - 7:59:55 AM

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  • HAL Id : hal-00968354, version 1
  • ARXIV : 1404.0141

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Alessio Figalli, Thomas Gallouët, Ludovic Rifford. On the convexity of injectivity domains on nonfocal manifolds. SIAM Journal on Mathematical Analysis, 2015, 47 (2), pp.969--1000. ⟨hal-00968354⟩

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