Asymptotic behaviour of λ-convex sets in the hyperbolic plane

被引：15

作者：

Gallego, E ^{[1
]}

Reventós, A ^{[1
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

来源：

GEOMETRIAE DEDICATA | 1999年 / 76卷 / 03期

关键词：

integral geometry; hyperbolic plane; lambda-convex set;

D O I：

10.1023/A:1005130211872

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that the limit Area/Length for a sequence of convex sets expanding over the whole hyperbolic plane is less than or equal 1, and exactly 1 when the sets considered are convex with respect to horocycles. We consider geodesics and horocycles as particular cases of curves of constant geodesic curvature lambda with 0 less than or equal to lambda less than or equal to 1 and we study the above limit Area/Length as a function of the parameter lambda.

引用

页码：275 / 289

页数：15