Twists and Gromov hyperbolicity of riemann surfaces

被引：0
作者：
Katsuhiko Matsuzaki
José M. Rodríguez
机构：
[1] Waseda University,Department of Mathematics, School of Education
[2] Universidad Carlos III de Madrid,Departamento de Matemáticas
来源：
Acta Mathematica Sinica, English Series | 2011年 / 27卷
关键词：
Quasiconformal maps; Riemann surfaces; Gromov hyperbolicity; 30F45; 53C23, 30C99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The main aim of this paper is to study whether the Gromov hyperbolicity is preserved under some transformations on Riemann surfaces (with their Poincaré metrics). We prove that quasiconformal maps between Riemann surfaces preserve hyperbolicity; however, we also show that arbitrary twists along simple closed geodesics do not preserve it, in general.
引用
收藏
页码：29 / 44
页数：15
相关论文
共 55 条
[1]  
Bonk M.(2000)Embeddings of Gromov hyperbolic spaces Geom. Funct. Anal. 10 266-306
[2]  
Schramm O.(2005)A product construction for hyperbolic metric spaces Illinois J. Math. 49 793-810
[3]  
Foertsch T.(2006)Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces Duke Math. J. 134 165-197
[4]  
Schroeder V.(2008)Gromov hyperbolic spaces and the sharp isoperimetric constant Invent. Math. 171 227-255
[5]  
Naor A.(2003)Geometric characterizations of Gromov hyperbolicity Invent. Math. 153 261-301
[6]  
Peres Y.(2003)Convexes hyperboliques et fonctions quasisymétriques Publ. Math. Inst. Hautes Études Sci. 97 181-237
[7]  
Schramm O.(2009)Symmetry and transitive properties of monohedral f-triangulations of the Riemannian sphere Acta Mathematica Sinica, English Series 25 1609-1616
[8]  
Wenger S.(2006)Gromov hyperbolicity of the Proc. Amer. Math. Soc. 134 1137-1142
[9]  
Balogh Z. M.(2010) and Bull. London Math. Soc. 42 282-294
[10]  
Buckley S. M.(2010) metrics Complex Var. Elliptic Equ. 55 127-135
123456