Noa Vikman: On the Existence of Harmonic Surfaces in Metric Spaces

As part of the rich study of harmonic maps from surfaces, the following question has been considered: Under what conditions is it possible to find a harmonic map in a given homotopy class? In an important contribution, Sacks and Uhlenbeck studies bubbling singularities and describes the existence of harmonic maps from 2-spheres into compact Riemannian manifolds. In this talk, I will formulate the same existence question in a metric setting, using Sobolev spaces of metric space valued maps. I will further describe some of the 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.