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arXiv · 2503.08553

Energy minimizing harmonic 2-spheres in metric spaces

Damaris Meier·Noa Vikman·Stefan Wenger
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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.

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Damaris Meier, Noa Vikman, Stefan Wenger. 2025-03-11. Energy minimizing harmonic 2-spheres in metric spaces. https://arxiv.org/abs/2503.08553

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