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Let be closed, bounded, convex sets. It is known that the monotonicity of the surface areas holds, i.e. . Here we give a quantitative estimate of the difference of the surface areas from below depending on the Hausdorff distance between and . 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 . Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), no. 3, pp. 327–333