The Quantitative Isoperimetric Inequality for Planar Convex Domains
Nitsch, Carlo
Bollettino dell'Unione Matematica Italiana, Tome 1 (2008), p. 573-589 / Harvested from Biblioteca Digitale Italiana di Matematica
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We prove that among all the convex bounded domains in ℝ2 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.

Publié le : 2008-10-01
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     author = {Carlo Nitsch},
     title = {The Quantitative Isoperimetric Inequality for Planar Convex Domains},
     journal = {Bollettino dell'Unione Matematica Italiana},
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     year = {2008},
     pages = {573-589},
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     language = {en},
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Nitsch, Carlo. The Quantitative Isoperimetric Inequality for Planar Convex Domains. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 573-589. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_3_573_0/

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