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

被引：0

作者：

Luo, Feng ^{[1
]}

Wu, Tianqi ^{[2
]}

机构：

[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[2] Harvard Univ, Ctr Math Sci & Applicat, Cambridge, MA 02138 USA

来源：

ADVANCES IN MATHEMATICS | 2024年 / 458卷

关键词：

Circle domains; Convex hull; Convex surfaces; Hyperbolic and conformal geometries; POLYHEDRAL SURFACES; UNIFORMIZATION;

D O I：

10.1016/j.aim.2024.109969

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：56

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