Harmonic branched coverings and uniformization of CAT(k) spheres-Reference-Cited by-同舟云学术

Harmonic branched coverings and uniformization of CAT(k) spheres

Published:2021-07-01 Issue:779 Volume:2021 Page:123-166
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Breiner Christine¹,Mese Chikako²

Affiliation:

1. Department of Mathematics , Fordham University , Bronx , New York , NY 10458 , USA

2. Department of Mathematics , Johns Hopkins University , 3400 N. Charles Street , Baltimore , MD 21218 , USA

Abstract

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 )

{(S,d)}

is a branched covering. As a consequence, if ( S , d )

{(S,d)}

is homeomorphically equivalent to the 2-sphere 𝕊 2

{\mathbb{S}^{2}}

, then it is conformally equivalent to 𝕊 2

{\mathbb{S}^{2}}

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2021-0031/pdf

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