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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
DOI: https://doi.org/10.1090/S0002-9939-2013-11627-8
Published electronically: April 3, 2013
MathSciNet review: 3056560
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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
  • 2. Alan F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics, vol. 91, Springer-Verlag, New York, 1983. MR 698777

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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-2013-11627-8
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.