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Convexity and the Average Curvature of Plane Curves (1997)

Lagarias, Jefferey C. ; Richardson, Thomas J.

Springer

Geometriae dedicata 67 (1997), S. 1-30

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ISSN: 1572-9168

Keywords: Average curvature ; total curvature ; convexity ; integral geometry ; plane curve ; geometric inequalities.

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1004912521664

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