Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem
Journal of the European Mathematical Society, Tome 5 (2003) no. 3, pp. 203-244
Voir la notice de l'article provenant de la source EMS Press
In this paper we present two upper bounds on the length of a shortest closed geodesic on compact Riemannian manifolds. The first upper bound depends on an upper bound on sectional curvature and an upper bound on the volume of the manifold. The second upper bound will be given in terms of a lower bound on sectional curvature, an upper bound on the diameter and a lower bound on the volume. The related questions that will also be studied are the following: given a contractible k-dimensional sphere in Mn, how fast can this sphere be contracted to a point, if pgri(Mn)={0} for 1lei
@article{JEMS_2003_5_3_a0,
author = {Alexander Nabutovsky and Regina Rotman},
title = {Upper bounds on the length of a shortest closed geodesic and quantitative {Hurewicz} theorem},
journal = {Journal of the European Mathematical Society},
pages = {203--244},
publisher = {mathdoc},
volume = {5},
number = {3},
year = {2003},
doi = {10.1007/s10097-003-0051-7},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10097-003-0051-7/}
}
TY - JOUR AU - Alexander Nabutovsky AU - Regina Rotman TI - Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem JO - Journal of the European Mathematical Society PY - 2003 SP - 203 EP - 244 VL - 5 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1007/s10097-003-0051-7/ DO - 10.1007/s10097-003-0051-7 ID - JEMS_2003_5_3_a0 ER -
%0 Journal Article %A Alexander Nabutovsky %A Regina Rotman %T Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem %J Journal of the European Mathematical Society %D 2003 %P 203-244 %V 5 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1007/s10097-003-0051-7/ %R 10.1007/s10097-003-0051-7 %F JEMS_2003_5_3_a0
Alexander Nabutovsky; Regina Rotman. Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem. Journal of the European Mathematical Society, Tome 5 (2003) no. 3, pp. 203-244. doi: 10.1007/s10097-003-0051-7
Cité par Sources :