The Busemann--Petty problem via spherical harmonics.
type: Item
instance of: scholarly article
title: The Busemann--Petty problem via spherical harmonics.
zbMATH Open document ID: 1034.52005
DOI: 10.1016/S0001-8708(02)00078-6
published in: Advances in Mathematics
publication date: 2003-07-30T00:00:00Z
review text: The Busemann-Petty problem asks whether inequalities between volumes of central hyperplane sections of centrally symmetric convex bodies in \(\mathbb{R}^n\) imply a corresponding inequality for the volumes of the bodies. The author gives a short new proof for the positive part \((n\leq 4)\) of the solution. This proof also employs the parallel section function, but avoids the use of intersection bodies. An essential tool are spherical harmonics and the Funk-Hecke theorem.
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 1957034
zbMATH Keywords: Busemann-Petty problem
zbMATH Keywords: sections of convex bodies
zbMATH Keywords: spherical harmonics
zbMATH Keywords: Funk-Hecke formula
author: Alexander Koldobsky
reviewed by: Rolf Schneider
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1957034