Hostname: page-component-7c8c6479df-7qhmt Total loading time: 0 Render date: 2024-03-29T13:51:17.758Z Has data issue: false hasContentIssue false

THE ROLE OF FUNNELS AND PUNCTURES IN THE GROMOV HYPERBOLICITY OF RIEMANN SURFACES

Published online by Cambridge University Press:  30 May 2006

Ana Portilla
Affiliation:
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad, 30, 28911 Leganés, Madrid, Spain (apferrei@math.uc3m.es; jomaro@math.uc3m.es; etouris@math.uc3m.es)
José M. Rodríguez
Affiliation:
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad, 30, 28911 Leganés, Madrid, Spain (apferrei@math.uc3m.es; jomaro@math.uc3m.es; etouris@math.uc3m.es)
Eva Tourís
Affiliation:
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad, 30, 28911 Leganés, Madrid, Spain (apferrei@math.uc3m.es; jomaro@math.uc3m.es; etouris@math.uc3m.es)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove results on geodesic metric spaces which guarantee that some spaces are not hyperbolic in the Gromov sense. We use these theorems in order to study the hyperbolicity of Riemann surfaces. We obtain a criterion on the genus of a surface which implies non-hyperbolicity. We also include a characterization of the hyperbolicity of a Riemann surface $S^*$ obtained by deleting a closed set from one original surface $S$. In the particular case when the closed set is a union of continua and isolated points, the results clarify the role of punctures and funnels (and other more general ends) in the hyperbolicity of Riemann surfaces.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2006