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Convexity and the Average Curvature of Plane Curves |
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| Authors: | Jefferey C Lagarias Thomas J Richardson |
| Institution: | (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. |
| Keywords: | Average curvature total curvature convexity integral geometry plane curve geometric inequalities |
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