Compact non-orientable surfaces of genus 6 with extremal metric discs
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- by Gou Nakamura
- Conform. Geom. Dyn. 20 (2016), 218-234
- DOI: https://doi.org/10.1090/ecgd/298
- Published electronically: June 20, 2016
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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 only by $g$. We discuss how many extremal discs are embedded in non-orientable extremal surfaces of genus 6. This is the final genus in our interest because it is already known for $g=3, 4, 5$, or $g>6$. We show that non-orientable extremal surfaces of genus 6 admit at most two extremal discs. The locus of extremal discs is also obtained for each surface. Consequently non-orientable extremal surfaces of arbitrary genus $g\geqq 3$ admit at most two extremal discs. Furthermore we determine the groups of automorphisms of non-orientable extremal surfaces of genus 6 with two extremal discs.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): October 10, 2015
- Received by editor(s) in revised form: February 17, 2016
- Published electronically: June 20, 2016
- Additional Notes: This work was partially supported by the JSPS KAKENHI Grant No. 25400147.
- © Copyright 2016 American Mathematical Society
- Journal: Conform. Geom. Dyn. 20 (2016), 218-234
- MSC (2010): Primary 30F50; Secondary 30F40, 05C10
- DOI: https://doi.org/10.1090/ecgd/298
- MathSciNet review: 3513567
Dedicated: Dedicated to Professor Noriaki Suzuki on the occasion of his sixtieth birthday