A sharp isoperimetric inequality in the plane (Q610660)
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scientific article; zbMATH DE number 5825389
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sharp isoperimetric inequality in the plane |
scientific article; zbMATH DE number 5825389 |
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A sharp isoperimetric inequality in the plane (English)
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10 December 2010
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Summary: We show that among all the convex bounded domains in \({\mathbb R}^2\) having a fixed Fraenkel asymmetry index, there exists only one convex set (up to similarity) which minimizes the isoperimetric deficit. We also show how to construct this set. The result can be read as a sharp improvement of the isoperimetric inequality for convex planar domains.
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isoperimetric inequality
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Bonnesen-style inequality
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Fraenkel asymmetry
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isoperimetric deficit
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