The length of a shortest closed geodesic and the area of a -dimensional sphere

Author:
R. Rotman

Journal:
Proc. Amer. Math. Soc. **134** (2006), 3041-3047

MSC (2000):
Primary 53C22; Secondary 58E10

Published electronically:
April 10, 2006

MathSciNet review:
2231630

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Riemannian manifold homeomorphic to . The purpose of this paper is to establish the new inequality for the length of a shortest closed geodesic, , in terms of the area of . 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

Email:
rotman@math.psu.edu, rina@math.toronto.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08297-9

Keywords:
Geometric inequalities,
closed geodesics

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

Article copyright:
© Copyright 2006
American Mathematical Society