The Busemann--Petty problem via spherical harmonics.

DOI10.1016/S0001-8708(02)00078-6zbMath1034.52005MaRDI QIDQ1399567

Alexander L. Koldobsky

Publication date: 30 July 2003

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

spherical harmonicsBusemann-Petty problemsections of convex bodiesFunk-Hecke formula

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

The measure-comparison problem for polar \((p, \mu)\)-centroid bodies, Generalizations of the Busemann-Petty problem for sections of convex bodies, On the \(L_p\) dual Minkowski problem, The lower dimensional Busemann-Petty problem for bodies with the generalized axial symmetry, Intersection bodies and generalized cosine transforms, Starshaped sets, The Cos\(^\lambda\) and Sin\(^\lambda\) transforms as intertwining operators between generalized principal series representations of SL\((n+1,\mathbb K)\), On the generalized Busemann-Petty problem, The complex Busemann-Petty problem on sections of convex bodies, Local properties of intertwining operators on the sphere, The Busemann--Petty problem in hyperbolic and spherical spaces, The Minkowski problem in Gaussian probability space, Asymptotics of convex sets in Euclidean and hyperbolic spaces, The Busemann–Petty problem in the complex hyperbolic space, \(L_p\) intersection bodies

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