Volume difference inequalities

DOI10.1090/tran/7173zbMath1387.52014arXiv1608.03435OpenAlexW2963861981MaRDI QIDQ4608781

Alexander L. Koldobsky, Apostolos Giannopoulos

Publication date: 28 March 2018

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

Full work available at URL: https://arxiv.org/abs/1608.03435

zbMATH Keywords

Busemann-Petty problemintersection bodiesconvex bodiesShephard problemisotropic convex bodysection volumesprojection volumesvolume difference inequalities

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Asymptotic theory of Banach spaces (46B06)

Related Items

The measure-comparison problem for polar \((p, \mu)\)-centroid bodies, Sylvester-Busemann type functionals with respect to Orlicz centroid bodies, Stability related to the Lp$L_p$ Busemann–Petty problem, Applications of sections and half volumes in stability, A variant of the \(L_p\)-Shephard problem via \((p,q)\)-projection bodies

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A hyperplane inequality for measures of convex bodies in \(\mathbb R^{n }, \; n\leq 4\)
• Stability inequalities for projections of convex bodies
• Stability in the Busemann-Petty and Shephard problems
• Isomorphic properties of intersection bodies
• Estimates for measures of lower dimensional sections of convex bodies
• Maximum and minimum sets for some geometric mean values
• Dual mixed volumes and the slicing problem
• On convex perturbations with a bounded isotropic constant
• Intersection bodies and dual mixed volumes
• An application of the Fourier transform to sections of star bodies
• Projections of convex bodies and the Fourier transform
• Stability and slicing inequalities for intersection bodies
• Isoperimetric inequalities and identities for \(k\)-dimensional cross-sections of convex bodies
• The dual Brunn-Minkowski theory for bounded Borel sets: dual affine quermassintegrals and inequalities
• Slicing inequalities for measures of convex bodies
• Zu einem Problem von Shephard über die Projektionen konvexer Körper
• Slicing inequalities for subspaces of $L_p$
• Bounding marginal densities via affine isoperimetry
• Volume Ratios and a Reverse Isoperimetric Inequality
• On High Dimensional Maximal Functions Associated to Convex Bodies
• Approximation of the Sphere by Polytopes having Few Vertices
• Convolutions, Transforms, and Convex Bodies
• Shadows of Convex Bodies
• Intersection bodies, positive definite distributions, and the Busemann-Petty problem
• Variants of the Busemann–Petty Problem and of the Shephard Problem
• Sections of Convex Bodies
• Stability and Separation in Volume Comparison Problems
• M-Estimates for Isotropic Convex Bodies and Their L q -Centroid Bodies
• Asymptotic Geometric Analysis, Part I
• A Remark on Measures of Sections of $$\boldsymbol{L}_{p}$$ -balls
• Convex Bodies The Brunn-MinkowskiTheory