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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The length of a shortest closed geodesic and the area of a $2$-dimensional sphere
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by R. Rotman PDF
Proc. Amer. Math. Soc. 134 (2006), 3041-3047 Request permission

Abstract:

Let $M$ be a Riemannian manifold homeomorphic to $S^2$. The purpose of this paper is to establish the new inequality for the length of a shortest closed geodesic, $l(M)$, in terms of the area $A$ of $M$. This result improves previously known inequalities by C.B. Croke (1988), by A. Nabutovsky and the author (2002) and by S. Sabourau (2004).
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Additional Information
  • R. Rotman
  • Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 – and – Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
  • MR Author ID: 659650
  • Email: rotman@math.psu.edu, rina@math.toronto.edu
  • Received by editor(s): February 24, 2005
  • Received by editor(s) in revised form: April 14, 2005
  • Published electronically: April 10, 2006
  • Communicated by: Jon G. Wolfson
  • © Copyright 2006 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3041-3047
  • MSC (2000): Primary 53C22; Secondary 58E10
  • DOI: https://doi.org/10.1090/S0002-9939-06-08297-9
  • MathSciNet review: 2231630