(1) AT & T Labs–Research, Florham Park, NJ, 07932, U.S.A.;(2) Bell Laboratories, Murray Hill, NJ, 07974, U.S.A.
Abstract:
The average curvature of a rectifiable closed curve in R2 is its total absolute curvature divided by its length. If a rectifiable closed curve in R2 is contained in the interior of a convex set D then its average curvature is at least as large as the average curvature of the simple closed curve D which bounds the convex set.