双曲 3 空间凸面的科贝猜想和韦尔问题

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2024-10-15 DOI:10.1016/j.aim.2024.109969

Feng Luo , Tianqi Wu

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引用次数: 0

摘要

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。

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

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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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.