Prime ends for domains in metric measure spaces and their use in potential theory and QC theory

(7 mai 2021 / May 7, 2021) Séminaire Montreal Analysis Seminar

Nages Shanmugalingam (University of Cincinnati, USA)
Prime ends for domains in metric measure spaces and their use in potential theory and QC theory

Abstract: Prime ends were first developed by Caratheodory in order to understand the boundary behavior of conformal mappings from the disk. As such, the construction of Caratheodory and Ahlfors worked for simply connected planar domains but had to be modified for more general domains. In this talk, we will focus on a construction in the setting of domains in metric spaces, and describe their use in potential theory (Dirichlet problem for the p-energy minimizers) and in studying boundary behavior of QC maps.