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Strong displacement convexity on Riemannian manifolds

Strong displacement convexity on Riemannian manifolds Ricci curvature bounds in Riemannian geometry are known to be equivalent to the weak convexity (convexity along at least one geodesic between any two points) of certain functionals in the space of probability measures. We prove that the weak convexity can be reinforced into strong (usual) convexity, thus solving a question left open in Lott and Villani (Ann of Math, to appear). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Strong displacement convexity on Riemannian manifolds

Mathematische Zeitschrift , Volume 257 (2) – May 8, 2007

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Springer-Verlag
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-007-0124-5
Publisher site
See Article on Publisher Site

Abstract

Ricci curvature bounds in Riemannian geometry are known to be equivalent to the weak convexity (convexity along at least one geodesic between any two points) of certain functionals in the space of probability measures. We prove that the weak convexity can be reinforced into strong (usual) convexity, thus solving a question left open in Lott and Villani (Ann of Math, to appear).

Journal

Mathematische ZeitschriftSpringer Journals

Published: May 8, 2007

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