On tangent cones in Wasserstein space

Lott, John

doi:10.1090/proc/13415

On tangent cones in Wasserstein space
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Proc. Amer. Math. Soc. 145 (2017), 3127-3136 Request permission

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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