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Inequalities for the Surface Area of Projections of Convex Bodies

  • Apostolos Giannopoulos (a1), Alexander Koldobsky (a2) and Petros Valettas (a2)

Abstract

We provide general inequalities that compare the surface area $S(K)$ of a convex body $K$ in ${{\mathbb{R}}^{n}}$ to the minimal, average, or maximal surface area of its hyperplane or lower dimensional projections. We discuss the same questions for all the quermassintegrals of $K$ . We examine separately the dependence of the constants on the dimension in the case where $K$ is in some of the classical positions or $K$ is a projection body. Our results are in the spirit of the hyperplane problem, with sections replaced by projections and volume by surface area.

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Inequalities for the Surface Area of Projections of Convex Bodies

  • Apostolos Giannopoulos (a1), Alexander Koldobsky (a2) and Petros Valettas (a2)

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