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An intrinsic parallel transport in Wasserstein space


Author: John Lott
Journal: Proc. Amer. Math. Soc. 145 (2017), 5329-5340
MSC (2010): Primary 51K10, 58J99
DOI: https://doi.org/10.1090/proc/13655
Published electronically: July 10, 2017
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Abstract: If $ M$ is a smooth compact connected Riemannian manifold, let $ P(M)$ denote the Wasserstein space of probability measures on $ M$. We describe a geometric construction of parallel transport of some tangent cones along geodesics in $ P(M)$. We show that when everything is smooth, the geometric parallel transport agrees with earlier formal calculations.


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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/13655
Received by editor(s): August 9, 2016
Received by editor(s) in revised form: January 6, 2017
Published electronically: July 10, 2017
Additional Notes: This research was partially supported by NSF grant DMS-1207654 and a Simons Fellowship
Communicated by: Guofang Wei
Article copyright: © Copyright 2017 American Mathematical Society