An intrinsic parallel transport in Wasserstein space

Lott, John

doi:10.1090/proc/13655

An intrinsic parallel transport in Wasserstein space
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Proc. Amer. Math. Soc. 145 (2017), 5329-5340 Request permission

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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