Linear bounds for lengths of geodesic loops on riemannian 2-spheres

Alexander Nabutovsky University of Toronto Regina Rotman University of Toronto

Differential Geometry mathscidoc:1609.10239

Journal of Differential Geometry, 89, (2), 217-232, 2011
Let M be a closed surface diffeomorphic to S2 endowed with a Riemannian metric. Denote the diameter of M by d. We prove that for every x 2 M and every positive integer k there exist k distinct geodesic loops based at x of length  20kd.
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@inproceedings{alexander2011linear,
  title={LINEAR BOUNDS FOR LENGTHS OF GEODESIC LOOPS ON RIEMANNIAN 2-SPHERES},
  author={Alexander Nabutovsky, and Regina Rotman},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913210454428217900},
  booktitle={Journal of Differential Geometry},
  volume={89},
  number={2},
  pages={217-232},
  year={2011},
}
Alexander Nabutovsky, and Regina Rotman. LINEAR BOUNDS FOR LENGTHS OF GEODESIC LOOPS ON RIEMANNIAN 2-SPHERES. 2011. Vol. 89. In Journal of Differential Geometry. pp.217-232. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913210454428217900.
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