Geodesic
A sharp isoperimetric inequality in the plane
Journal of the European Mathematical Society, Tome 13 (2011) no. 1, pp. 185-206.

Voir la notice de l'article provenant de la source EMS Press

We show that among all the convex bounded domain in R2 having an assigned Fraenkel asymmetry index, there exists only one convex set (up to a 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 domain.
DOI : 10.4171/jems/248
Classification : 52-XX, 49-XX, 00-XX
Keywords: Isoperimetric inequality, Bonnesen-style inequality, Fraenkel asymmetry, isoperimetric deficit 
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Angelo Alvino; Vincenzo Ferone; Carlo Nitsch. A sharp isoperimetric inequality in the plane. Journal of the European Mathematical Society, Tome 13 (2011) no. 1, pp. 185-206. doi : 10.4171/jems/248. http://geodesic.mathdoc.fr/articles/10.4171/jems/248/

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