Energy minimizing harmonic 2-spheres in metric spaces
Differential Geometry
2025-03-12 v1 Metric Geometry
Abstract
In their seminal 1981 article, Sacks-Uhlenbeck famously proved the existence of non-trivial harmonic 2-spheres in every closed Riemannian manifold with non-zero second homotopy group. Their arguments heavily rely on PDE techniques. The purpose of the present paper is to develop a conceptually simple metric approach to the existence of harmonic spheres. This allows us to generalize the Sacks-Uhlenbeck result to a large class of compact metric spaces.
Keywords
Cite
@article{arxiv.2503.08553,
title = {Energy minimizing harmonic 2-spheres in metric spaces},
author = {Damaris Meier and Noa Vikman and Stefan Wenger},
journal= {arXiv preprint arXiv:2503.08553},
year = {2025}
}