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On the Maximum Curvature of Closed Curves in Negatively Curved Manifolds
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2015
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