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Conformal Geometry and Dynamics

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Compact non-orientable hyperbolic surfaces with an extremal metric disc

Authors: Ernesto Girondo and Gou Nakamura
Journal: Conform. Geom. Dyn. 11 (2007), 29-43
MSC (2000): Primary 30F50; Secondary 30F40
Published electronically: March 8, 2007
MathSciNet review: 2295996
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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.

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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

Gou Nakamura
Affiliation: Science Division, Center for General Education, Aichi Institute of Technology, Yakusa-Cho, Toyota 470-0392, Japan
MR Author ID: 639802

Keywords: Extremal discs, Kleinian surfaces
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.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.