Harmonic branched coverings and uniformization of CAT(k) spheres
2021 ◽
Vol 0
(0)
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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 ) {(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}} .
2007 ◽
Vol 142
(2)
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pp. 259-268
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2018 ◽
Vol 27
(05)
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pp. 1850030
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2008 ◽
Vol 17
(07)
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pp. 787-816
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