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Gromov Hyperbolicity of Riemann Surfaces

Gromov Hyperbolicity of Riemann Surfaces
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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. 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.
作者 José M.RODRíGUEZ EVa TOURIS
机构地区 Departamento de Matemáticas
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第2期209-228,共20页 数学学报（英文版）
基金 supported by a grant from DGI(BFM 2003-04870)Spain supported by a grant from DGI(BFM 2000-0022)Spain
关键词 Gromov hyperbolicity hyperbolic Riemann surface Gromov hyperbolicity hyperbolic Riemann surface
分类号 O174.51 [理学—基础数学]
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参考文献32

  • 1Alvarez, V., Pestana, D., Rodriguez, J. M.: Isoperimetric inequalities in Riemann surfaces of infinite type.Rev. Mat. Iberoamericana, 15, 353-427 (1999)
  • 2Alvarez, V., Rodriguez, J. M., Yakubovich, V. A.: Subadditivity of p-harmonic "measure" on graphs.Michigan Math. J., 49, 47-64 (2001)
  • 3Canton, A., Fernandez, J. L., Pestana, D., Rodriguez, J. M.: On harmonic functions on trees. Potential Anal., 15, 199-244 (2001)
  • 4Fernandez, J. L., Rodriguez, J. M.: Area growth and Green's function of Riemann surfaces. Arkiv Mat.,30, 83-92 (1992)
  • 5Holopainen, I., Soardi, P. M.: p-harmonic functions on graphs and manifolds. Manuscripta Math., 94,95-110 (1997)
  • 6Kanai, M.: Rough isometries and combinatorial approximations of geometries of non-compact Riemannian manifolds. J. Math. Soc. Japan, 37, 391-413 (1985)
  • 7Kanai, M.: Rough isometries and the parabolicity of Riemannian manifolds. J. Math. Soc. Japan, 38,227-238 (1986)
  • 8Kanai, M.: Analytic inequalities and rough isometries between non-compact Riemannian manifolds. Curvature and Topology of Riemannian manifolds (Katata, 1985). Lecture Notes in Math., 1201, 122-137(1986)
  • 9Rodriguez, J. M.: Isoperimetric inequalities and Dirichlet functions of Riemann surfaces. Publicacions Matematiques, 38, 243-253 (1994)
  • 10Rodriguez, J. M.: Two remarks on Riemann surfaces. Publicacions Matemdtiques, 38, 463-477 (1994)
Acta Mathematica Sinica,English Series
2007年 第2期

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