Publication:
Gromov hyperbolicity of Riemann surfaces

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URI: https://hdl.handle.net/10016/6451
ISSN: 1439-8516 (Print)
ISSN: 1439-7617 (Online)
DOI: 10.1007/s10114-005-0547-z
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gromov_touris_ams_2007_ps.pdf (332.02 KB)
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2007-02
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Springer
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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.
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20 pages, no figures.-- MSC2000 codes: 30F, 30F20, 30F45.
MR#: MR2286916 (2007k:30080)
Zbl#: Zbl 1115.30050
Keywords
Gromov hyperbolicity, Hyperbolic Riemann surface
Bibliographic citation
Acta Mathematica Sinica (Engl. Ser.), 2007, vol. 23, n. 2, p. 209-228
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