The Busemann--Petty problem in hyperbolic and spherical spaces

DOI10.1016/j.aim.2005.05.003zbMath1112.52007arXivmath/0410501OpenAlexW1999776594MaRDI QIDQ2497330

Yanyan Li

Publication date: 4 August 2006

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

Full work available at URL: https://arxiv.org/abs/math/0410501

zbMATH Keywords

Fourier transform

Mathematics Subject Classification ID

Spherical and hyperbolic convexity (52A55) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (21)

The spherical convex floating body ⋮ On sections of convex bodies in hyperbolic space ⋮ Generalized intersection bodies ⋮ The lower dimensional Busemann-Petty problem in the complex hyperbolic space ⋮ Stability and slicing inequalities for intersection bodies ⋮ Busemann's intersection inequality in hyperbolic and spherical spaces ⋮ \(L_p\) Busemann-Petty centroid inequality in hyperbolic and spherical spaces ⋮ Spherical centroid bodies ⋮ Stability related to the Lp$L_p$ Busemann–Petty problem ⋮ Starshaped sets ⋮ On the generalized Busemann-Petty problem ⋮ Modified Busemann-Petty problem on sections of convex bodies ⋮ Generalized intersection bodies are not equivalent ⋮ The complex Busemann-Petty problem on sections of convex bodies ⋮ The Lower Dimensional Busemann‐Petty Problem with Weights ⋮ A solution to the lower dimensional Busemann-Petty problem in the hyperbolic space ⋮ The isomorphic Busemann-Petty problem for \(s\)-concave measures ⋮ Uniqueness results for bodies of constant width in the hyperbolic plane ⋮ The Busemann–Petty problem in the complex hyperbolic space ⋮ The dual Brunn-Minkowski inequalities in spherical and hyperbolic spaces ⋮ The Busemann-Petty problem on entropy of log-concave functions

Cites Work

• Intersection bodies and dual mixed volumes
• An application of the Fourier transform to sections of star bodies
• A positive solution to the Busemann-Petty problem in \(\mathbb{R}^4\)
• An analytic solution to the Busemann-Petty problem on sections of convex bodies
• A generalization of the Busemann-Petty problem on sections of convex bodies
• The Busemann--Petty problem via spherical harmonics.
• On spherically convex univalent functions
• The Busemann-Petty problem for arbitrary measures
• On the derivatives of X-ray functions
• Generalizations of the Busemann-Petty problem for sections of convex bodies
• Modified Busemann-Petty problem on sections of convex bodies
• Intersection bodies, positive definite distributions, and the Busemann-Petty problem
• The Brunn-Minkowski inequality
• A functional analytic approach to intersection bodies
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