Convexity and the average curvature of plane curves (Q1366276)
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scientific article; zbMATH DE number 1059626
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convexity and the average curvature of plane curves |
scientific article; zbMATH DE number 1059626 |
Statements
Convexity and the average curvature of plane curves (English)
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25 May 1998
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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.
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convexity
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plane curve
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geometric inequalities
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total curvature
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average curvature
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