Speaker: Mohammad Reza Pakzad
Title: Rigidity of weak solutions to Monge-Ampere equations
Abstract: In this talk, we will explore rigidity of the weak solutions to the Monge-Amp\`ere equation, by replacing the Hessian determinant by other weaker variants, without any a priori convexity assumptions. Some past and recent results and their proofs concerning rigid behaviour (e.g. convexity or developabilty) of Sobolev solutions in two and higher dimensions will be discussed. We will also study the rigidity of solutions with H\”older continuous derivatives. We will contrast these results with some some non-rigidity statements recently proved by the speaker and M. Lewicka using convex integration.