Geodesic
A Sharp Quantitative Estimate for the Perimeters of Convex Sets in the Plane
Journal of convex analysis, Tome 22 (2015) no. 3, pp. 853-858
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Let $E \subset B \subset \mathbb R^2$ be bounded, convex sets. The monotonicity of the perimeters holds, i.e. $\mathcal{H}^{1} (\partial E) \leqslant \mathcal{H}^{1}(\partial B)$. Here we give a quantitative estimate of the difference of the perimeters: it shows how much the perimeter of $B$ increases when $B$ becomes larger and larger with respect to $E$. We give an example showing that our estimate is sharp.
Classification : 52A10
Mots-clés : Convex sets, perimeters, Hausdorff distance 
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     author = {M. Carozza and F. Giannetti and F. Leonetti and A. Passarelli di Napoli},
     title = {A {Sharp} {Quantitative} {Estimate} for the {Perimeters} of {Convex} {Sets} in the {Plane}},
     journal = {Journal of convex analysis},
     pages = {853--858},
     year = {2015},
     volume = {22},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_3_JCA_2015_22_3_a13/}
}
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M. Carozza; F. Giannetti; F. Leonetti; A. Passarelli di Napoli. A Sharp Quantitative Estimate for the Perimeters of Convex Sets in the Plane. Journal of convex analysis, Tome 22 (2015) no. 3, pp. 853-858. http://geodesic.mathdoc.fr/item/JCA_2015_22_3_JCA_2015_22_3_a13/