CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Inequalities for the surface area of projections of convex bodies

  • Apostolos Giannopoulos,
    Department of Mathematics, University of Athens, Panepistimioupolis 157-84, Athens, Greece
  • Alexander Koldobsky,
    Department of Mathematics, University of Missouri, Columbia, MO, USA
  • Petros Valettas,
    Department of Mathematics, University of Missouri, Columbia, MO, USA
Format:   LaTeX   MathJax   PDF  

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.
Keywords: surface area, convex body, projection surface area, convex body, projection
MSC Classifications: 52A20, 46B05 show english descriptions Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
unknown classification 46B05
52A20 - Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
46B05 - unknown classification 46B05
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/