University of Cincinnati
Talk Title: Modulus of sets of finite perimeter and quasiconformal maps between metric spaces of globally Q-bounded geometry
Abstract: In Euclidean space, it is well-known that quasiconformal maps quasi-preserve the n-modulus of curves. In 1973, Kelly also showed that the n/(n-1)-modulus of surfaces is quasi-preserved. We generalize this result to the setting of Ahlfors Q-regular metric spaces supporting a 1-Poincaré inequality. In fact, we consider a larger class of surfaces so our results are new even in Euclidean space. This talk is based on joint work with Panu Lahti and Nageswari Shanmugalingam.