Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Gold Open Access
Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173


Compact non-orientable surfaces of genus $ 4$ with extremal metric discs

Author: Gou Nakamura
Journal: Conform. Geom. Dyn. 13 (2009), 124-135
MSC (2000): Primary 30F50; Secondary 30F40
Published electronically: April 22, 2009
MathSciNet review: 2497316
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 30F50, 30F40

Retrieve articles in all journals with MSC (2000): 30F50, 30F40

Additional Information

Gou Nakamura
Affiliation: Science Division, Center for General Education, Aichi Institute of Technology, Yakusa-Cho, Toyota 470-0392, Japan

PII: S 1088-4173(09)00194-5
Keywords: Extremal discs, Klein surfaces
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).
Dedicated: Dedicated to Professor Yoshihiro Mizuta on the occasion of his 60th birthday
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia