A partial optimal transport functional in an isoperimetric problem

Davide Carazzato (University of Vienna)

Abstract: We consider a shape optimization problem of isoperimetric type, containing a repulsive term defined in term of an optimal transport problem. We provide a brief introduction about the basic geometric properties of the partial optimal transport term, and we focus on its maximizers to sustain the intuition about its repulsive nature. In fact, through a symmetrization technique, we show that the unique maximizer of the optimal transport term is the ball, in complete competition with the perimeter term. This is based on a joint work with Almut Burchard and Ihsan Topaloglu.