The length of a shortest closed geodesic and the area of a  -dimensional sphere |
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| Authors: | R Rotman |
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| Institution: | Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 -- and -- Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3 |
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| 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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| Keywords: | Geometric inequalities closed geodesics |
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