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, ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe
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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  • 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, Society for Industrial and Applied Mathematics, 2015, 47 (2), pp.969--1000. ⟨hal-00968354⟩

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