The length of a shortest closed geodesic and the area of a $2$-dimensional sphere
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- by R. Rotman
- Proc. Amer. Math. Soc. 134 (2006), 3041-3047
- DOI: https://doi.org/10.1090/S0002-9939-06-08297-9
- Published electronically: April 10, 2006
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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).References
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Bibliographic 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