Compact non-orientable hyperbolic surfaces with an extremal metric disc
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- by Ernesto Girondo and Gou Nakamura PDF
- Conform. Geom. Dyn. 11 (2007), 29-43 Request permission
Abstract:
The size of a metric disc embedded in a compact non-orientable hyperbolic surface is bounded by some constant depending only on the genus $g \ge 3$. We show that a surface of genus greater than six contains at most one metric disc of the largest radius. For the case $g=3$, we carry out an exhaustive study of all the extremal surfaces, finding the location of every extremal disc inside them.References
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Additional Information
- Ernesto Girondo
- Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Address at time of publication: Departamento de Matemáticas, IMAFF, CSIC, Madrid, Spain
- MR Author ID: 650820
- ORCID: 0000-0002-9611-9721
- Email: ernesto.girondo@uam.es
- Gou Nakamura
- Affiliation: Science Division, Center for General Education, Aichi Institute of Technology, Yakusa-Cho, Toyota 470-0392, Japan
- MR Author ID: 639802
- Email: gou@aitech.ac.jp
- Received by editor(s): September 5, 2006
- Published electronically: March 8, 2007
- Additional Notes: The first author was supported in part by the MCyT research project BFM2003-04964.
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn. 11 (2007), 29-43
- MSC (2000): Primary 30F50; Secondary 30F40
- DOI: https://doi.org/10.1090/S1088-4173-07-00157-9
- MathSciNet review: 2295996