Mathematical Physics and Harmonic Analysis Seminar
Date: October 23, 2020
Time: 1:50PM - 2:50PM
Location: Zoom
Speaker: Jun Kitagawa, Michigan State University
Title: On free discontinuities in optimal transport
Abstract: It is well known that regularity results for the optimal transport (Monge-Kantorovich) problem require rigid geometric restrictions. In this talk, we consider the structure of the set of ``free discontinuities'' which arise when transporting mass from a connected domain to a disconnected one, and show regularity of this set, along with a stability result under suitable perturbations of the target measure. These are based on a non-smooth implicit function theorem for convex functions, which is of independent interest. This talk is based on joint work with Robert McCann (Univ. of Toronto).