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 University Press

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
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