Compact non-orientable surfaces of genus $4$ with extremal metric discs
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- by Gou Nakamura
- Conform. Geom. Dyn. 13 (2009), 124-135
- DOI: https://doi.org/10.1090/S1088-4173-09-00194-5
- Published electronically: April 22, 2009
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Abstract:
A compact hyperbolic surface of genus $g$ is said to be extremal if it admits an extremal disc, a disc of the largest radius determined by $g$. We know how many extremal discs are embedded in a non-orientable extremal surface of genus $g=3$ or $g>6$. We show in the present paper that there exist $144$ non-orientable extremal surfaces of genus $4$, 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 $g=3$.References
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Bibliographic Information
- 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): March 27, 2008
- Published electronically: April 22, 2009
- Additional Notes: This work was supported in part by Grant-in-Aid for Young Scientists (B) (No. 20740081).
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn. 13 (2009), 124-135
- MSC (2000): Primary 30F50; Secondary 30F40
- DOI: https://doi.org/10.1090/S1088-4173-09-00194-5
- MathSciNet review: 2497316
Dedicated: Dedicated to Professor Yoshihiro Mizuta on the occasion of his 60th birthday