On the (In)stability of the Identity Map in Optimal Transportation

Yash Jhaveri

Abstract: We collect some examples of optimal transports in order to explore the (in)stability of the identity map as an optimal transport. First, we consider density and domain perturbations near regular portions of domains. Second, we investigate density and domains deformations to non-regular parts of domains. Here, we restrict our attention to two dimensions and focus near 90 degree corners.