Conformality of quasiconformal mappings at a point, revisited

2018/02/26 by Shishikura, Mitsuhiro · 1 citation
#30C62 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.09137

Abstract

We present a new and simple proof of Teichmüller-Wittich-Belinskii's and Gutlyanskii-Martio's theorems on the conformality of quasiconformal mappings at a given point. Known proofs gave separate estimates for the radial and angular variations, but our proof unifies them using Grötzsch-type inequality for the variation of cross-ratio of four points on the Riemann sphere. We also give a sufficient condition for C^1+α-conformality

Cited by

• Integrable Teichmüller spaces for analysis on Weil-Petersson curves

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