The character of Thurston's circle packings

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外文摘要：We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently,some quite simple criteria are obtained for the existence of hyperbolic circle packings.For example,if a closed surface X admits a circle packing with all the vertex degrees di≥7,then it admits a unique complete hyperbolic metric so that the triangulation graph of the circle packing is isotopic to a geometric decomposition of X.This criterion is sharp due to the fact that any closed hyperbolic surface admits no triangulations with all d i≤6.As a corollary,we obtain a new proof of the uniformization theorem for closed surfaces with genus g≥2;moreover,any hyperbolic closed surface has a geometric decomposition.To obtain our results,we use Chow-Luo's combinatorial Ricci flow as a fundamental tool.

外文关键词：

charactercircle packingscombinatorial Ricci flow

作者：

Huabin Ge、Aijin Lin

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作者单位：

School of Mathematics,Renmin University of China,Beijing 100872,China

Department of Mathematics,National University of Defense Technology,Changsha 410073,China

基金：

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaHunan Provincial Natural Science Foundation of ChinaHunan Provincial Natural Science Foundation of ChinaScientific Research Program Funds of National University of Defense Technology

项目编号：

1187109412122119121714802020JJ46582022JJ1005922-ZZCX-016

出版年：

2024

DOI：

10.1007/s11425-023-2182-2

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(7)