On displacement interpolation of measures involved in Brenier’s theorem
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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.References
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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
- MR Author ID: 841634
- ORCID: 0000-0002-1258-3034
- Email: nicolas.juillet@math.unistra.fr
- 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
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 3623-3632
- MSC (2010): Primary 28A75
- DOI: https://doi.org/10.1090/S0002-9939-2011-10891-8
- MathSciNet review: 2813392