Periodicity and circle packings of the hyperbolic plane

被引：24

作者：

Bowen, L ^{[1
]}

机构：

[1] Dept Math, Davis, CA 95616 USA

来源：

GEOMETRIAE DEDICATA | 2003年 / 102卷 / 01期

基金：

美国国家科学基金会;

关键词：

circle packing; densest packings; hyperbolic plane; invariant measures; optimal density;

D O I：

10.1023/B:GEOM.0000006580.47816.e9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that given a fixed radius r, the set of isometry-invariant probability measures supported on 'periodic' radius r-circle packings of the hyperbolic plane is dense in the space of all isometry-invariant probability measures on the space of radius r-circle packings. By a periodic packing, we mean one with cofinite symmetry group. As a corollary, we prove the maximum density achieved by isometry-invariant probability measures on a space of radius r-packings of the hyperbolic plane is the supremum of densities of periodic packings. We also show that the maximum density function varies continuously with radius.

引用

页码：213 / 236

页数：24

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