Let E ⊂ B ⊂ R 2 be bounded, convex sets. The monotonicity of the perimeters holds, i.e. H^1(∂E) \leq H^1(∂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.
A sharp quantitative estimate for the perimeters of convex sets in the plane / Carozza, Menita; Giannetti, Flavia; Leonetti, Francesco; PASSARELLI DI NAPOLI, Antonia. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 22:3(2015), pp. 853-858.
A sharp quantitative estimate for the perimeters of convex sets in the plane
GIANNETTI, FLAVIA;PASSARELLI DI NAPOLI, ANTONIA
2015
Abstract
Let E ⊂ B ⊂ R 2 be bounded, convex sets. The monotonicity of the perimeters holds, i.e. H^1(∂E) \leq H^1(∂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.File in questo prodotto:
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