Geodesic
On the Maximum Curvature of Closed Curves in Negatively Curved Manifolds
Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 713-722

Voir la notice de l'article provenant de la source Cambridge

DOI

Motivated by Almgren’s work on the isoperimetric inequality, we prove a sharp inequality relating the length and maximum curvature of a closed curve in a complete, simply connected manifold of sectional curvature at most −1. Moreover, if equality holds, then the norm of the geodesic curvature is constant and the torsion vanishes. The proof involves an application of the maximum principle to a function defined on pairs of points.
DOI : 10.4153/CMB-2015-030-3
Mots-clés : 53C20, manifold, curvature 
Brendle, Simon; Chodosh, Otis. On the Maximum Curvature of Closed Curves in Negatively Curved Manifolds. Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 713-722. doi: 10.4153/CMB-2015-030-3
@article{10_4153_CMB_2015_030_3,
     author = {Brendle, Simon and Chodosh, Otis},
     title = {On the {Maximum} {Curvature} of {Closed} {Curves} in {Negatively} {Curved} {Manifolds}},
     journal = {Canadian mathematical bulletin},
     pages = {713--722},
     year = {2015},
     volume = {58},
     number = {4},
     doi = {10.4153/CMB-2015-030-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-030-3/}
}
TY  - JOUR
AU  - Brendle, Simon
AU  - Chodosh, Otis
TI  - On the Maximum Curvature of Closed Curves in Negatively Curved Manifolds
JO  - Canadian mathematical bulletin
PY  - 2015
SP  - 713
EP  - 722
VL  - 58
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-030-3/
DO  - 10.4153/CMB-2015-030-3
ID  - 10_4153_CMB_2015_030_3
ER  - 
%0 Journal Article
%A Brendle, Simon
%A Chodosh, Otis
%T On the Maximum Curvature of Closed Curves in Negatively Curved Manifolds
%J Canadian mathematical bulletin
%D 2015
%P 713-722
%V 58
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-030-3/
%R 10.4153/CMB-2015-030-3
%F 10_4153_CMB_2015_030_3

Cité par Sources :