Harmonic maps into singular spaces
Organizers
Speaker
Time
Tuesday, March 18, 2025 2:45 PM - 4:30 PM
Venue
A3-4-301
Online
Zoom 815 762 8413
(BIMSA)
Abstract
The study of harmonic map into singular spaces (Riemannian simplical complex) was initiated by Gromov-Schoen, as an application, they obtained superrigidity result of p-adic representation of lattice of isometry group of Quaternionic hyperbolic space and Cayley plane. Later, the analysis of harmonic maps into general non-positively curved (NPC) metric spaces was substantially established by Korevaar-Schoen in a series of papers. In this talk, we consider the energy minimizing maps from a Lipschitz Riemannian domain into a CAT(1)-space, we shall discuss the regularity problem of such maps. As applications, we first generalize the Sacks-Uhlenbeck’s result into a singular setting, secondly, we will talk about a Liouville type theorem. This is based on a series work with Christine Breiner, Aliana Fraser, Lan-Hsuan Huang, Chikako Mese, Pam Sargent, and Brian Freidin.