Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 48, No. 1, pp. 303-308 (2007)
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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 curvesShengliang Pan and Hong ZhangDepartment of Mathematics, East China Normal University, Shanghai, 200062, P. R. China, e-mail: slpan@math.ecnu.edu.cnAbstract: 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 Full text of the article:
Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.
© 2007 Heldermann Verlag
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