Convexity and the average curvature of plane curves
Let the average curvature \(M(\gamma)\) of a rectifiable closed curve \(\gamma\) in the Euclidean plane be its total absolute curvature divided by its length. The main result is: Let \(D\) be a compact convex set in the Euclidean plane with nonempty interior. If \(\gamma\) is any closed rectifiable curve contained in \(D\), then \((\partial D)\leq M(\gamma)\). This result improves inequalities given by I. Fáry, resp. L. A. Santaló.
scientific article; zbMATH DE number 1059626