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Proceedings of the American Mathematical Society

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On tangent cones in Wasserstein space


Author: John Lott
Journal: Proc. Amer. Math. Soc. 145 (2017), 3127-3136
MSC (2010): Primary 51K99
DOI: https://doi.org/10.1090/proc/13415
Published electronically: December 8, 2016
MathSciNet review: 3637959
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Abstract: If $M$ is a smooth compact Riemannian manifold, let $P(M)$ denote the Wasserstein space of probability measures on $M$. If $S$ is an embedded submanifold of $M$, and $\mu$ is an absolutely continuous measure on $S$, then we compute the tangent cone of $P(M)$ at $\mu$.


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Additional Information

John Lott
Affiliation: Department of Mathematics, University of California - Berkeley, Berkeley, California 94720-3840
MR Author ID: 116090
ORCID: 0000-0002-5107-8719
Email: lott@berkeley.edu

Received by editor(s): March 9, 2016
Received by editor(s) in revised form: August 6, 2016
Published electronically: December 8, 2016
Additional Notes: This research was partially supported by NSF grant DMS-1207654 and a Simons Fellowship
Communicated by: Guofang Wei
Article copyright: © Copyright 2016 American Mathematical Society