JournalsrlmVol. 27, No. 3pp. 327–333

A sharp quantitative estimate for the surface areas of convex sets in R3\mathbb R^3

  • Menita Carozza

    Università del Sannio, Benvento, Italy
  • Flavia Giannetti

    Università degli Studi di Napoli Federico II, Italy
  • Francesco Leonetti

    Università degli Studi dell'Aquila, Italy
  • Antonia Passarelli di Napoli

    Università degli Studi di Napoli Federico II, Italy
A sharp quantitative estimate for the surface areas of convex sets in $\mathbb R^3$ cover

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Abstract

Let EBR3E \subset B \subset \mathbb R^3 be closed, bounded, convex sets. It is known that the monotonicity of the surface areas holds, i.e. H2(E)H2(B)\mathcal{H}^{2}(\partial E) \leqslant \mathcal{H}^{2}(\partial B). Here we give a quantitative estimate of the difference of the surface areas from below depending on the Hausdorff distance between EE and BB. Moreover, we construct an example which shows the sharpness of our result.

Cite this article

Menita Carozza, Flavia Giannetti, Francesco Leonetti, Antonia Passarelli di Napoli, A sharp quantitative estimate for the surface areas of convex sets in R3\mathbb R^3. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), no. 3, pp. 327–333

DOI 10.4171/RLM/737