Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below

Abstract

We prove existence and uniqueness of optimal maps on $RC{D}^{\ast }(K,N)$ spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation.

10 pages

Cited by in corpus (1)

• On Interpolation and Curvature via Wasserstein Geodesics