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