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.
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Lagarias, J.C., Richardson, T.J. Convexity and the Average Curvature of Plane Curves. Geometriae Dedicata 67, 1–30 (1997). https://doi.org/10.1023/A:1004912521664
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DOI: https://doi.org/10.1023/A:1004912521664