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Compact non-orientable hyperbolic surfaces with an extremal metric disc
Author(s):
Ernesto
Girondo;
Gou
Nakamura
Journal:
Conform. Geom. Dyn.
11
(2007),
29-43.
MSC (2000):
Primary 30F50;
Secondary 30F40
Posted:
March 8, 2007
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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  . We show that a surface of genus greater than six contains at most one metric disc of the largest radius. For the case  , 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
Email:
ernesto.girondo@uam.es
Gou
Nakamura
Affiliation:
Science Division, Center for General Education, Aichi Institute of Technology, Yakusa-Cho, Toyota 470-0392, Japan
Email:
gou@aitech.ac.jp
DOI:
10.1090/S1088-4173-07-00157-9
PII:
S 1088-4173(07)00157-9
Keywords:
Extremal discs,
Kleinian surfaces
Received by editor(s):
September 5, 2006
Posted:
March 8, 2007
Additional Notes:
The first author was supported in part by the MCyT research project BFM2003-04964.
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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