广义John Gromov双曲域与映射的扩展

Pub Date : 2021-11-30 DOI:10.7146/math.scand.a-128968

Qingshan Zhou, Liulan Li, A. Rasila

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引用次数: 1

摘要

设$\Omega \subset \mathbb{R}^n$为格罗莫夫双曲，$\varphi$长度的约翰域。我们证明了$\Omega$的内边界与具有可视度量的Gromov边界之间存在一致连续的恒等式，利用这一结果，我们不仅证明了拟共形同纯的边界连续性，而且证明了具有拟双曲度量的域之间更一般的粗糙拟等距的边界连续性。

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Generalized John Gromov hyperbolic domains and extensions of maps

Let $\Omega \subset \mathbb{R}^n$ be a Gromov hyperbolic, $\varphi$-length John domain. We show that there is a uniformly continuous identification between the inner boundary of $\Omega$ and the Gromov boundary endowed with a visual metric, By using this result, we prove the boundary continuity not only for quasiconformal homeomorphisms, but also for more generally rough quasi-isometries between the domains equipped with the quasihyperbolic metrics.

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