Open Access
October 2011 Linear bounds for lengths of geodesic loops on Riemannian 2-spheres
Alexander Nabutovsky, Regina Rotman
J. Differential Geom. 89(2): 217-232 (October 2011). DOI: 10.4310/jdg/1324477410


Let $M$ be a closed surface diffeomorphic to $S^2$ endowed with a Riemannian metric. Denote the diameter of $M$ by $d$. We prove that for every $x \in M$ and every positive integer $k$ there exist $k$ distinct geodesic loops based at $x$ of length $\le 20kd$.


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Alexander Nabutovsky. Regina Rotman. "Linear bounds for lengths of geodesic loops on Riemannian 2-spheres." J. Differential Geom. 89 (2) 217 - 232, October 2011.


Published: October 2011
First available in Project Euclid: 21 December 2011

zbMATH: 1243.53075
MathSciNet: MR2863917
Digital Object Identifier: 10.4310/jdg/1324477410

Rights: Copyright © 2011 Lehigh University

Vol.89 • No. 2 • October 2011
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