Geometric distortion properties of quasiconformal maps

Abstract: Quasiconformal maps are orientation-preserving homeomorphisms that have nice geometric distortion properties; infinitesimally, they map circles to ellipses with uniformly bounded eccentricity. This local distortion property turns out to have significant implications for the global properties of the maps and will impose a certain degree of regularity. In this talk, we will look at the most extreme stretching and rotation behavior that a quasiconformal map can have, and we will build extremizers that have this behavior on as large a set as possible. This will improve upon results of Astala-Iwaniec-Prause-Saksman and Hitruhin, and will (in a sense) show what the worst possible behavior is.

Host: John McCarthy