On the Maximum Curvature of Closed Curves in Negatively Curved Manifolds
On the Maximum Curvature of Closed Curves in Negatively Curved Manifolds
Abstract Motivated by Almgrenās 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 ā1. Moreover, if equality holds, then the norm of the geodesic curvature is constant and ā¦