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A characterization of Gromov hyperbolicity of surfaces with variable negative curvature

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URI: https://hdl.handle.net/10016/6445
ISSN: 0214-1493
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characterization_touris_pm_2009_ps.pdf (255.67 KB)
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2009
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Universitat Autònoma de Barcelona, Departament de Matemàtiques
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Abstract
In this paper we show that, in order to check Gromov hyperbolicity of any surface with curvature $K \leq -k^2 < 0$, we just need to verify the Rips condition on a very small class of triangles, namely, those contained in simple closed geodesics. This result is, in fact, a new characterization of Gromov hyperbolicity for this kind of surfaces.
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18 pages, 4 figures.-- MSC2000 codes: 53C15, 53C21, 53C22, 53C23.
MR#: MR2474116 (2009k:53091)
Zbl#: Zbl 1153.53320
Keywords
Gromov hyperbolicity, Riemannian surface, Negatively curved Riemannian surface
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Publicacions Matemàtiques, 2009, vol. 53, n. 1, p. 83-110
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