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Inequalities for the Surface Area of Projections of Convex Bodies

Published online by Cambridge University Press:  20 November 2018

Apostolos Giannopoulos ,
Alexander Koldobsky  and
Petros Valettas
Apostolos Giannopoulos
Affiliation:
Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis 157-84, Athens, Greece email: apgiannop@math.uoa.gr
Alexander Koldobsky
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO, USA email: koldobskiya@missouri.eduvalettasp@missouri.edu
Petros Valettas
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO, USA email: koldobskiya@missouri.eduvalettasp@missouri.edu
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Abstract

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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.

Keywords

52A2046B05surface areaconvex bodyprojection
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 4 , 01 August 2018 , pp. 804 - 823
Copyright
Copyright © Canadian Mathematical Society 2018

References

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