Prohibiting isolated singularities in optimal transport

Abstract

We give natural topological conditions on the support of the target measure under which solutions to the optimal transport problem with cost function satisfying the (weak) Ma, Trudinger, and Wang condition cannot have any isolated singular points.

10 pages, minor correction in proof of Lemma 3.3

References in corpus (1)

• Continuity and injectivity of optimal maps for non-negatively cross-curved costs