Title
On the Existence of Harmonic Surfaces in Metric Spaces
Abstract
In an important contribution to the rich study of harmonic maps from surfaces, Sacks and Uhlenbeck describe the existence of harmonic maps from 2-spheres into manifolds with non-trivial second fundamental group. Their approach builds on estimates computed using PDE techniques that do not extend to a metric setting. In this talk, I will describe some key concepts that allow us to generalize some of the results of Sacks-Uhlenbeck to a wide class of metric spaces. This is based on joint work with Damaris Meier and Stefan Wenger.
