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

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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

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