Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 1, pp. 303-308 (2007)

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A reverse isoperimetric inequality for convex plane curves

Shengliang Pan and Hong Zhang

Department of Mathematics, East China Normal University, Shanghai, 200062, P. R. China, e-mail:

Abstract: In this note we present a reverse isoperimetric inequality for closed convex curves, which states that if $\gamma$ is a closed strictly convex plane curve with length $L$ and enclosing an area $A$, then one gets \[L^2\le4\pi (A + |\tilde{A}|),\] where $\tilde{A}$ denotes the oriented area of the domain enclosed by the locus of curvature centers of $\gamma$, and the equality holds if and only if $\gamma$ is a circle.

Keywords: convex curves, Minkowski's support function, locus of centers of curvature, integral of radius of curvature, reverse isoperimetric inequality

Classification (MSC2000): 52A38, 52A40

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Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.

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