拟共形映射在一点上的共形性
Conformality of quasiconformal mappings at a point, revisited
摘要：
给出了Teichmüller-Wittich-Belinskii和Gutlyanskiii-Martio关于拟共形映射在给定点的共形性定理的一个新的简单证明.已知的证明给出了径向和角度变化的单独估计，但我们的证明使用黎曼球面上四个点的交比变化的Grötzsch型不等式将它们统一起来。我们还给出了$C^{1+α}$ -共形的一个充分条件
英文摘要：
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
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