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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Geometry of Riemann surfaces based on
closed geodesics


Author: Paul Schmutz Schaller
Journal: Bull. Amer. Math. Soc. 35 (1998), 193-214
MSC (1991): Primary 30F45, 53C22, 57M50, 11F06, 11H99; Secondary 32G15, 11F72
MathSciNet review: 1609636
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Abstract | References | Similar Articles | Additional Information

Abstract: The paper presents a survey on recent results on the geometry of Riemann surfaces showing that the study of closed geodesics provides a link between different aspects of Riemann surface theory such as hyperbolic geometry, topology, spectral theory, and the theory of arithmetic Fuchsian groups. Of particular interest are the systoles, the shortest closed geodesics of a surface; their study leads to the hyperbolic geometry of numbers with close analogues to classical sphere packing problems.


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Additional Information

Paul Schmutz Schaller
Email: Paul.Schmutz@maths.unine.ch

DOI: http://dx.doi.org/10.1090/S0273-0979-98-00750-2
PII: S 0273-0979(98)00750-2
Received by editor(s): October 1, 1997
Received by editor(s) in revised form: March 19, 1998
Additional Notes: Partially supported by Schweizerischer Nationalfonds.
Article copyright: © Copyright 1998 American Mathematical Society