On the Busemann-Petty problem\\ concerning central sections\\ of centrally symmetric convex bodies

DOI10.1090/S0273-0979-1994-00493-8zbMath0814.52003arXivmath/9404230OpenAlexW2009144789MaRDI QIDQ4299217

Richard J. Gardner

Publication date: 29 June 1994

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9404230

zbMATH Keywords

volumeinequalitiesconvex bodiescentrally symmetricEuclidean \(n\)-space

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Radon transform (44A12) Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume, other geometric measure theory (28A75) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (3) dimensions (including convex surfaces) (52A15) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items

The dual \(\phi\)-Brunn-Minkowski inequality, Functional analytic characterizations of classes of convex bodies, New inequalities for star bodies, On intersection and mixed intersection bodies, \(L_p\)-mixed intersection bodies and star duality, \(q\)-dual mixed volumes and \(L_{p}\)-intersection bodies, Dual Orlicz-Brunn-Minkowski theory, Lipschitz star bodies, Intersection bodies and ellipsoids, The dual Orlicz-Minkowski problem, Starshaped sets, On dual quermassintegrals of mixed intersection bodies, On mixed complex intersection bodies, Characterizations of \(l_\infty^n\) and \(l_1^n\), and their stabilities, \(L_p\) intersection bodies, \(L_{p}\)-mixed intersection bodies, The Cramer-Rao inequality for star bodies, Stability estimates for star bodies in terms of their intersection bodies, Dual kinematic formulas

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Central sections of centrally symmetric convex bodies
• Intersection bodies and dual mixed volumes
• Unsolved problems in geometry
• On the Busemann-Petty problem for perturbations of the ball
• Tomography of convex and star bodies
• A positive answer to the Busemann-Petty problem in three dimensions
• Functional analytic characterizations of classes of convex bodies
• Volume in terms of concurrent cross-sections
• Problems on convex bodies
• Volumes and Areas of Cross-Section
• A note on a problem of H. Busemann and C. M. Petty concerning sections of symmetric convex bodies
• On the Busemann‐Petty problem about convex, centrally symmetric bodies in
• The existence of a centrally symmetric convex body with central sections that are unexpectedly small
• Intersection Bodies and the Busemann-Petty Problem
• Radialpotenzintegrale zentralsymmetrischer Rotationskörper und Ungleichheitsaussagen Busemannscher Art.
• A Note on a Problem of Busemann.
• Infinitesimal Aspects of the Busemann-Petty Problem
• Convexity