The Koebe conjecture and the Weyl problem for convex surfaces in hyperbolic 3-space

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-15 DOI:10.1016/j.aim.2024.109969

Feng Luo , Tianqi Wu

引用次数: 0

Abstract

We prove that the Koebe circle domain conjecture is equivalent to the Weyl type problem that every complete hyperbolic surface of genus zero is isometric to the boundary of the hyperbolic convex hull of the complement of a circle domain in the hyperbolic 3-space. Applications of the result to discrete conformal geometry will be discussed. The main tool we use is Schramm's transboundary extremal lengths.

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双曲 3 空间凸面的科贝猜想和韦尔问题

我们证明了 Koebe 圆域猜想等同于韦尔型问题，即每个零属的完整双曲面与双曲 3 空间中圆域补集的双曲凸壳边界等距。我们将讨论这一结果在离散共形几何中的应用。我们使用的主要工具是施拉姆的跨边界极值长度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.