Abstract

We establish the existence of Euclidean tangent cones on Wasserstein spaces over compact Alexandrov spaces of curvature bounded below. By using this Riemannian structure, we formulate and construct gradient flows of functions on such spaces. If the underlying space is a Riemannian manifold of nonnegative sectional curvature, then our gradient flow of the free energy produces a solution of the linear Fokker-Planck equation.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 475-516
Launched on MUSE
2009-03-20
Open Access
No
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