Laboratoire J.A. Dieudonné
Université Côte d’Azur
12/01/2023 – h. 2 p.m.
Title: Mass Transportation and Convex Earth Theorem
Abstract: We address the problem of regularity of optimal transport maps with respect to quadratic geodesic distances on Riemannian manifolds. We explain how the so-called Transport Continuity Property is related with convexity properties of injectivity domains of exponential mappings. Then, we present the Convex Earth Theorem which shows that, in a certain sense, almost round spheres look convex.