具有薄膨胀的拟共形映射

Pub Date : 2022-07-01 DOI:10.5565/publmat6622207

C. Bishop

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引用次数: 0

摘要

.我们给出了一个估计，它量化了这样一个事实，即其扩张仅在一组小面积上为非零的归一化拟共形映射在整个平面上均匀地近似恒等式。精确的陈述是由作者的拟共形折叠方法在构造整个函数中的应用所推动的；特别是Fagella、Godillon和Jarque[7]给出的超验游荡域的构造。

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Quasiconformal maps with thin dilatations

. We give an estimate that quantiﬁes the fact that a normalized quasi-conformal map whose dilatation is non-zero only on a set of small area approximates the identity uniformly on the whole plane. The precise statement is motivated by applications of the author’s quasiconformal folding method for constructing entire functions; in particular a construction of transcendental wandering domains given by Fagella, Godillon and Jarque [7].

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