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arXiv · 2011.12802

Harmonic branched coverings and uniformization of CAT($k$) spheres

Christine Breiner·Chikako Mese
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Abstract

Let $S$ be a surface with a metric $d$ satisfying an upper curvature bound in the sense of Alexandrov (i.e. via triangle comparison). We show that an almost conformal harmonic map from a surface into $(S,d)$ is a branched covering. As a consequence, if $(S,d)$ is homeomorphically equivalent to the 2-sphere $\mathbb S^2$, then it is conformally equivalent to $\mathbb S^2$.

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Christine Breiner, Chikako Mese. 2020-11-25. Harmonic branched coverings and uniformization of CAT($k$) spheres. https://arxiv.org/abs/2011.12802

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