Nitsch: The Quantitative Isoperimetric Inequality for Planar Convex Domains

Nitsch, Carlo:
The Quantitative Isoperimetric Inequality for Planar Convex Domains
Bollettino dell'Unione Matematica Italiana Serie 9 1 (2008), fasc. n.3, p. 573-589, (English)
pdf (457 Kb), djvu (167 Kb). | MR 2455332 | Zbl 1190.26025

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We prove that among all the convex bounded domains in $\mathbb{R}^2$ having an assigned Fraenkel asymmetry index, there exists only one convex set (up to a similarity) which minimizes the isoperimetric deficit. We 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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Referenze Bibliografiche