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arXiv · 1802.09137

Conformality of quasiconformal mappings at a point, revisited

Mitsuhiro Shishikura
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Abstract

We present a new and simple proof of Teichm\"uller-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 Gr\"otzsch-type inequality for the variation of cross-ratio of four points on the Riemann sphere. We also give a sufficient condition for $C^{1+\alpha}$-conformality

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Mitsuhiro Shishikura. 2018-02-26. Conformality of quasiconformal mappings at a point, revisited. https://arxiv.org/abs/1802.09137

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