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The length of a shortest closed geodesic and the area of a $ 2$-dimensional sphere

Author(s): R. Rotman
Journal: Proc. Amer. Math. Soc. 134 (2006), 3041-3047.
MSC (2000): Primary 53C22; Secondary 58E10
Posted: 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).

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A. Nabutovsky and R. Rotman, The length of a shortest closed geodesic on a $ 2$-dimensional sphere, IMRN, 2002 (2002), no. 39, 2121-2129.

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A. Nabutovsky and R. Rotman, Volume, diameter and the minimal mass of a stationary $ 1$-cycle, GAFA, 14 (2004), 748-790. MR 2084979 (2005g:53069)

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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: 10.1090/S0002-9939-06-08297-9
PII: S 0002-9939(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
Posted: April 10, 2006
Communicated by: Jon G. Wolfson
Copyright of article: Copyright 2006, American Mathematical Society

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