Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6463

 Google™ Scholar. Others By: Portilla, Ana - Rodríguez, José M. - Tourís, Eva
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 Title: The topology of balls and Gromov hyperbolicity of Riemann surfaces Author(s): Portilla, AnaRodríguez, José M.Tourís, Eva Publisher: Elsevier Issued date: Nov-2004 Citation: Differential Geometry and its Applications, 2004, vol. 21, n. 3, p. 317-335 URI: http://hdl.handle.net/10016/6463 ISSN: 0926-2245 DOI: 10.1016/j.difgeo.2004.05.006 Description: 19 pages, no figures.-- MSC2000 codes: 30F20, 30F45, 53C23.MR#: MR2091367 (2005e:53057)Zbl#: Zbl 1070.30019 Abstract: We prove that every ball in any non-exceptional Riemann surface with radius less or equal than $\frac 1 2\log 3$ is either simply or doubly connected. We use this theorem in order to study the hyperbolicity in the Gromov sense of Riemann surfaces. The results clarify the role of punctures and funnels of a Riemann surface in its hyperbolicity. Sponsor: Research by first two authors (A.P. and J.M.R.) was partially supported by a grant from DGI (BFM 2000-0022), Spain. Research by third author (E.T.)was supported by a grant from DGI (BFM 2000-0022), Spain. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1016/j.difgeo.2004.05.006 Keywords: Gromov hyperbolicityRiemann surfaceFunnelPuncture Rights: © Elsevier Appears in Collections: DM - GAMA - Artículos de Revistas