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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
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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
Email: lott@berkeley.edu

DOI: https://doi.org/10.1090/proc/13415
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