THE ROLE OF FUNNELS AND PUNCTURES IN THE GROMOV HYPERBOLICITY OF RIEMANN SURFACES

Proceedings of the Edinburgh Mathematical Society

Ana Portilla¹ 

[1] José M. Rodríguez

关键词: Primary 30F20;    30F45;    hyperbolicity;    Riemann surface;    funnel;    puncture;   

DOI  :  10.1017/S0013091504001555

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We prove results on geodesic metric spaces which guarantee that some spaces are not hyperbolic in the Gromov sense. We use these theorems in order to study the hyperbolicity of Riemann surfaces. We obtain a criterion on the genus of a surface which implies non-hyperbolicity. We also include a characterization of the hyperbolicity of a Riemann surface $S^*$ obtained by deleting a closed set from one original surface $S$. In the particular case when the closed set is a union of continua and isolated points, the results clarify the role of punctures and funnels (and other more general ends) in the hyperbolicity of Riemann surfaces.

【 授权许可】

Unknown