Filling Radius and Short Closed Geodesics of the 2 -Sphere

Stéphane Sabourau

Bulletin de la Société Mathématique de France (2004)

  • Volume: 132, Issue: 1, page 105-136
  • ISSN: 0037-9484

Abstract

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We show that the length of the shortest nontrivial curve among the simple closed geodesics of index zero or one and the figure-eight geodesics of null index provides a lower bound on the area and the diameter of the Riemannian 2 -spheres.

How to cite

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Sabourau, Stéphane. "Filling Radius and Short Closed Geodesics of the $2$-Sphere." Bulletin de la Société Mathématique de France 132.1 (2004): 105-136. <http://eudml.org/doc/272430>.

@article{Sabourau2004,
abstract = {We show that the length of the shortest nontrivial curve among the simple closed geodesics of index zero or one and the figure-eight geodesics of null index provides a lower bound on the area and the diameter of the Riemannian $2$-spheres.},
author = {Sabourau, Stéphane},
journal = {Bulletin de la Société Mathématique de France},
keywords = {filling radius; closed geodesics; $1$-cycles},
language = {eng},
number = {1},
pages = {105-136},
publisher = {Société mathématique de France},
title = {Filling Radius and Short Closed Geodesics of the $2$-Sphere},
url = {http://eudml.org/doc/272430},
volume = {132},
year = {2004},
}

TY - JOUR
AU - Sabourau, Stéphane
TI - Filling Radius and Short Closed Geodesics of the $2$-Sphere
JO - Bulletin de la Société Mathématique de France
PY - 2004
PB - Société mathématique de France
VL - 132
IS - 1
SP - 105
EP - 136
AB - We show that the length of the shortest nontrivial curve among the simple closed geodesics of index zero or one and the figure-eight geodesics of null index provides a lower bound on the area and the diameter of the Riemannian $2$-spheres.
LA - eng
KW - filling radius; closed geodesics; $1$-cycles
UR - http://eudml.org/doc/272430
ER -

References

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