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arXiv · 1009.3881

The topology of balls and Gromov hyperbolicity of Riemann surfaces

Jesús Gonzalo Pérez·Ana Portilla·José M Rodríguez·Eva Tourís
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Abstract

For each k > 0 we find an explicit function f_k such that the topology of S inside the ball B(p,r) is `bounded' by f_k(r) for every complete Riemannian surface (compact or noncompact) with K\geq -k^2, every point p on the surface, and every r. Using this result, we obtain a characterization (simple to check in practical cases) of the Gromov hyperbolicity of a Riemann surface S* (with its own Poincaré metric) obtained by deleting from one original surface S any uniformly separated union of continua and isolated points.

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Jesús Gonzalo Pérez, Ana Portilla, José M Rodríguez, Eva Tourís. 2010-09-20. The topology of balls and Gromov hyperbolicity of Riemann surfaces. https://arxiv.org/abs/1009.3881

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