Hostname: page-component-7c8c6479df-8mjnm Total loading time: 0 Render date: 2024-03-29T09:33:47.385Z Has data issue: false hasContentIssue false

On extremal Riemann surfaces and their uniformizing fuchsian groups

Published online by Cambridge University Press:  01 January 2002

Ernesto Girondo
Affiliation:
Depto. de Matemáticas, Fac. de Ciencias, Universidad Autónoma de Madrid, C. Universitaria de Cantoblanco, E28049 Madrid, Spain e-mail: ernesto.girondo@uam.es, gabino.gonzalez@uam.es
Gabino González-Diez
Affiliation:
Depto. de Matemáticas, Fac. de Ciencias, Universidad Autónoma de Madrid, C. Universitaria de Cantoblanco, E28049 Madrid, Spain e-mail: ernesto.girondo@uam.es, gabino.gonzalez@uam.es
Rights & Permissions [Opens in a new window]

Extract

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.

Compact hyperbolic surfaces of given genus g containing discs of the maximum radius have been studied from various points of view. In this paper we connect these different approaches and observe some properties of the Fuchsian groups uniformizing both compact and punctured extremal surfaces. We also show that extremal surfaces of genera g=2,3 may contain one or several extremal discs, while an extremal disc is necessarily unique for g \ge 4. Along the way we also construct explicit families of extremal surfaces, one of which turns out to be free of automorphisms.

Type
Research Article
Copyright
2002 Glasgow Mathematical Journal Trust