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Compact non-orientable surfaces of genus  with extremal metric discs
Author(s):
Gou
Nakamura
Journal:
Conform. Geom. Dyn.
13
(2009),
124-135.
MSC (2000):
Primary 30F50;
Secondary 30F40
Posted:
April 22, 2009
MathSciNet review:
2497316
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Abstract:
A compact hyperbolic surface of genus  is said to be extremal if it admits an extremal disc, a disc of the largest radius determined by  . We know how many extremal discs are embedded in a non-orientable extremal surface of genus  or  . We show in the present paper that there exist  non-orientable extremal surfaces of genus  , and find the locations of all extremal discs in those surfaces. As a result, each surface contains at most two extremal discs. Our methods used here are similar to those in the case of  .
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Additional Information:
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/S1088-4173-09-00194-5
PII:
S 1088-4173(09)00194-5
Keywords:
Extremal discs,
Klein surfaces
Received by editor(s):
March 27, 2008
Posted:
April 22, 2009
Additional Notes:
This work was supported in part by Grant-in-Aid for Young Scientists (B) (No. 20740081).
Dedicated:
Dedicated to Professor Yoshihiro Mizuta on the occasion of his 60th birthday
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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