The lower dimensional Busemann-Petty problem for bodies with the generalized axial symmetry

DOI10.1007/s11856-009-0089-7zbMath1190.52007arXivmath/0701317OpenAlexW2594362601MaRDI QIDQ2655759

Boris Rubin

Publication date: 26 January 2010

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701317

zbMATH Keywords

Busemann-Petty problemintersection bodiesMinkowski functionalradial functionstar bodiescentrally symmetric convex bodiescanonical anglesspherical Radon transformsgeneralized cosine transforms

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items

Comparing volumes by concurrent cross-sections of complex lines: a Busemann-Petty type problem, Comparison of volumes of convex bodies in real, complex, and quaternionic spaces, The lower dimensional Busemann-Petty problem in the complex hyperbolic space, Stability and slicing inequalities for intersection bodies, Stability related to the Lp$L_p$ Busemann–Petty problem, The Cos\(^\lambda\) and Sin\(^\lambda\) transforms as intertwining operators between generalized principal series representations of SL\((n+1,\mathbb K)\), Sections of convex bodies with symmetries, The complex Busemann-Petty problem on sections of convex bodies, The isomorphic Busemann-Petty problem for \(s\)-concave measures

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