On the (in)stability of the identity map in optimal transportation

On the (in)stability of the identity map in optimal transportation - Yash Jhaveri

Yash Jhaveri
Member, School of Mathematics
October 14, 2019

In the optimal transport problem, it is well-known that the geometry of the target domain plays a crucial role in the regularity of the optimal transport. In the quadratic cost case, for instance, Caffarelli showed that having a convex target domain is essential in guaranteeing the optimal transport’s continuity. In this talk, we shall explore how, quantitatively, important convexity is in producing continuous optimal transports.