The topology of balls and Gromov hyperbolicity of Riemann surfaces |
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Institution: | Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad, 30, Leganés 28911, Madrid, Spain |
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Abstract: | We prove that every ball in any non-exceptional Riemann surface with radius less or equal than 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. |
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Keywords: | 30F20 30F45 |
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