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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Geometry of Riemann surfaces based on closed geodesics
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by Paul Schmutz Schaller PDF
Bull. Amer. Math. Soc. 35 (1998), 193-214 Request permission


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:
  • Received by editor(s): October 1, 1997
  • Received by editor(s) in revised form: March 19, 1998
  • Additional Notes: Partially supported by Schweizerischer Nationalfonds.
  • © Copyright 1998 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 35 (1998), 193-214
  • MSC (1991): Primary 30F45, 53C22, 57M50, 11F06, 11H99; Secondary 32G15, 11F72
  • DOI:
  • MathSciNet review: 1609636