A new characterization of Gromov hyperbolicity for negatively curved surfaces
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In this paper we show that to check Gromov hyperbolicity of any surface of constant negative curvature, or, Riemann surface, we only need to verify the Rips condition on a very small class of triangles, namely, those obtained by marking three points in a simple closed geodesic. This result is, in fact, a new characterization of Gromov hyperbolicity for Riemann surfaces.
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Rodríguez, J. M.; and Tourís, E. “A new characterization of Gromov hyperbolicity for negatively curved surfaces”. Publicacions Matemàtiques, vol.VOL 50, no. 2, pp. 249-78, https://raco.cat/index.php/PublicacionsMatematiques/article/view/49967.
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