On tangent cones in Wasserstein space
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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 $\mu$.References
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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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3127-3136
- MSC (2010): Primary 51K99
- DOI: https://doi.org/10.1090/proc/13415
- MathSciNet review: 3637959