A CHARACTERIZATION OF GROMOV HYPERBOLICITY OF SURFACES WITH VARIABLE NEGATIVE CURVATURE

被引：50

作者：

Portilla, Ana ^{[1
]}

Touris, Eva ^{[1
]}

机构：

[1] Univ Carlos III Madrid, Dept Matemat, Madrid 28911, Spain

来源：

PUBLICACIONS MATEMATIQUES | 2009年 / 53卷 / 01期

关键词：

Gromov hyperbolicity; Riemannian surface; negatively curved Riemannian surface; RIEMANN SURFACES; HARMONIC-FUNCTIONS; ROUGH ISOMETRIES; INFINITE TYPE; MANIFOLDS; SPACES; DECOMPOSITION; INEQUALITIES; METRICS; DOMAINS;

D O I：

10.5565/PUBLMAT_53109_04

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we show that, in order to check Gromov hyperbolicity of any surface with curvature K <= -k(2) < 0, we just need to verify the Rips condition on a very small class of triangles, namely, those contained in simple closed geodesics. This result is, in fact, a new characterization of Gromov hyperbolicity for this kind of surfaces.

引用

页码：83 / 110

页数：28

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