| Gromov Hyperbolicity of Riemann Surfaces |
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| 作者姓名： | Jos&#; M. RODPIGUEZ Eva TOURIS |
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| 作者单位： | Departamento de Matemdticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legangs, Madrid, Spain |
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| 摘 要： | We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its ＂building block components＂. We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it. These results clarify how the decomposition of a Riemann surface into Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the surface and allow us to obtain global results from local information.
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| 关 键 词： | 双曲黎曼曲面 Gromov双曲率 拓扑 度量空间 |
| 收稿时间： | 10 November 2003 |
| 修稿时间： | 2003-11-102004-08-25 |
Gromov Hyperbolicity of Riemann Surfaces |
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| Jos&#; M. RODPIGUEZ Eva TOURIS.Gromov Hyperbolicity of Riemann Surfaces[J].Acta Mathematica Sinica,2007,23(2):209-228. |
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| Authors: | José M Rodríguez Eva Tourís |
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| Institution: | (1) Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain |
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| Abstract: | In this paper we study the hyperbolicity in the Gromov sense of Riemann surfaces. We
deduce the hyperbolicity of a surface from the hyperbolicity of its “building block components”. We
also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of
some graph associated with it. These results clarify how the decomposition of a Riemann surface into
Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the
surface and allow us to obtain global results from local information.
The first author’s research is partially supported by a grant from DGI (BFM 2003-04870), Spain
The second author’s research is partially supported by a grant from DGI (BFM 2000-0022), Spain |
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| Keywords: | Gromov hyperbolicity hyperbolic Riemann surface |
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