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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Length inequalities for Riemann surfaces


Author: A. F. Beardon
Journal: Proc. Amer. Math. Soc. 141 (2013), 2699-2702
MSC (2010): Primary 30F45; Secondary 30F35, 20H05, 20H10
Published electronically: April 3, 2013
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Abstract | References | Similar Articles | Additional Information

Abstract: We establish inequalities between the lengths of certain closed loops in the triply punctured sphere and in the twice-punctured disc.


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

  • 1. Lars V. Ahlfors, Complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1978. An introduction to the theory of analytic functions of one complex variable; International Series in Pure and Applied Mathematics. MR 510197 (80c:30001)
  • 2. Alan F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics, vol. 91, Springer-Verlag, New York, 1983. MR 698777 (85d:22026)

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Additional Information

A. F. Beardon
Affiliation: CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 OWB, United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11627-8
PII: S 0002-9939(2013)11627-8
Keywords: Riemann surfaces, hyperbolic metric, punctures
Received by editor(s): October 26, 2011
Published electronically: April 3, 2013
Communicated by: Mario Bonk
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.