Compact Klein surfaces of genus $5$ with a unique extremal disc
Author:
Gou Nakamura
Journal:
Conform. Geom. Dyn. 17 (2013), 39-46
MSC (2010):
Primary 30F50; Secondary 05C10
DOI:
https://doi.org/10.1090/S1088-4173-2013-00251-8
Published electronically:
February 28, 2013
MathSciNet review:
3027523
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: A compact (orientable or non-orientable) surface of genus $g$ is said to be extremal if it contains an extremal disc, that is, a disc of the largest radius determined only by $g$. The present paper concerns non-orientable extremal surfaces of genus $5$. We represent the surfaces as side-pairing patterns of a hyperbolic regular $24$-gon, that is, a generic fundamental region of an NEC group uniformizing each of the surfaces. We also describe the group of automorphisms of the surfaces with a unique extremal disc.
- Christophe Bavard, Disques extrémaux et surfaces modulaires, Ann. Fac. Sci. Toulouse Math. (6) 5 (1996), no. 2, 191–202 (French, with English and French summaries). MR 1413853
- Ernesto Girondo and Gou Nakamura, Compact non-orientable hyperbolic surfaces with an extremal metric disc, Conform. Geom. Dyn. 11 (2007), 29–43. MR 2295996, DOI https://doi.org/10.1090/S1088-4173-07-00157-9
- Troels Jørgensen and Marjatta Näätänen, Surfaces of genus $2$: generic fundamental polygons, Quart. J. Math. Oxford Ser. (2) 33 (1982), no. 132, 451–461. MR 679814, DOI https://doi.org/10.1093/qmath/33.4.451
- Gou Nakamura, Compact non-orientable surfaces of genus 4 with extremal metric discs, Conform. Geom. Dyn. 13 (2009), 124–135. MR 2497316, DOI https://doi.org/10.1090/S1088-4173-09-00194-5
- Gou Nakamura, Compact non-orientable surfaces of genus 5 with extremal metric discs, Glasg. Math. J. 54 (2012), no. 2, 273–281. MR 2911368, DOI https://doi.org/10.1017/S0017089511000589
- Gou Nakamura, http://aitech.ac.jp/~nakamura/sp.html.
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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
MR Author ID:
639802
Email:
gou@aitech.ac.jp
Received by editor(s):
April 16, 2012
Published electronically:
February 28, 2013
Additional Notes:
This work was supported by Grant-in-Aid for Young Scientists (B) (No. 20740081), Japan Society for the Promotion of Science.
Article copyright:
© Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
