Packing strips in the hyperbolic plane

被引：6

作者：

Marshall, TH ^{[1
]}

Martin, GJ ^{[1
]}

机构：

[1] Univ Auckland, Dept Math, Auckland, New Zealand

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2003年 / 46卷

关键词：

strip; horodisc; packing; density; hyperbolic plane; Fuchsian group;

D O I：

10.1017/S0013091502000081

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A strip of radius r in the hyperbolic plane is the set of points within distance r of a given geodesic. We define the density of a packing of strips of radius r and prove that this density cannot exceed S(r) = 3/pi sinh r arccosh (1 + 1/2 sinh(2)r). This bound is sharp for every value of r and provides sharp bounds on collaring theorems for simple geodesics on surfaces.

引用

页码：67 / 73

页数：7