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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

On displacement interpolation of measures involved in Brenier's theorem


Author: Nicolas Juillet
Journal: Proc. Amer. Math. Soc. 139 (2011), 3623-3632
MSC (2010): Primary 28A75
Published electronically: February 28, 2011
MathSciNet review: 2813392
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Abstract: We prove that in the Wasserstein space built over $ \mathbb{R}^d$ the subset of measures that does not charge the non-differentiability set of convex functions is not displacement convex. This completes the study of Gigli on the geometric structure of measures meeting the sharp hypothesis of the refined version of Brenier's Theorem.


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Additional Information

Nicolas Juillet
Affiliation: Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67000 Strasbourg, France
Email: nicolas.juillet@math.unistra.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10891-8
Keywords: Optimal transport, Wasserstein space, rectifiability
Received by editor(s): July 23, 2010
Received by editor(s) in revised form: August 31, 2010
Published electronically: February 28, 2011
Communicated by: Mario Bonk
Article copyright: © Copyright 2011 American Mathematical Society