Generalizations of the Busemann-Petty problem for sections of convex bodies
From MaRDI portal
Publication:1883600
DOI10.1016/j.jfa.2003.10.008zbMath1056.52004OpenAlexW2022214958MaRDI QIDQ1883600
Publication date: 13 October 2004
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2003.10.008
Radon transform (44A12) Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38)
Related Items
Comparison of volumes of convex bodies in real, complex, and quaternionic spaces, Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds, Generalized intersection bodies, The lower dimensional Busemann-Petty problem for bodies with the generalized axial symmetry, Funk, cosine, and sine transforms on Stiefel and Grassmann manifolds, The lower dimensional Busemann-Petty problem in the complex hyperbolic space, Dual Orlicz-Brunn-Minkowski theory, Norm estimates for \(k\)-plane transforms and geometric inequalities, Complex \(L_p\)-intersection bodies, Stability and slicing inequalities for intersection bodies, Intersection bodies and generalized cosine transforms, Stability related to the Lp$L_p$ Busemann–Petty problem, Rényi divergence and \(L_p\)-affine surface area for convex bodies, METHOD OF MEAN VALUE OPERATORS FOR RADON TRANSFORMS IN THE SPACE OF MATRICES, New affine measures of symmetry for convex bodies, Isomorphic properties of intersection bodies, Divergence for \(s\)-concave and log concave functions, The Radon transform on the Heisenberg group and the transversal Radon transform, The Cos\(^\lambda\) and Sin\(^\lambda\) transforms as intertwining operators between generalized principal series representations of SL\((n+1,\mathbb K)\), Gaussian measure of sections of dilates and translations of convex bodies, Sections of convex bodies with symmetries, Semyanistyi's integrals and Radon transforms on matrix spaces, 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, Relative entropies for convex bodies, The Lower Dimensional Busemann‐Petty Problem with Weights, Comparison of volumes by means of the areas of central sections, The Busemann--Petty problem in hyperbolic and spherical spaces, Isomorphic Busemann-Petty problem for sections of proportional dimensions, On the Negative Solutions of L_p-Busemann-Petty Problem, The Busemann-Petty problem on entropy of log-concave functions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Invariant valuations on star-shaped sets
- Inequalities between intrinsic volumes
- Intersection bodies and dual mixed volumes
- On the Busemann-Petty problem for perturbations of the ball
- A short solution to the Busemann-Petty problem
- The Radon transform.
- 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
- Continuous rotation invariant valuations on convex sets
- The Busemann--Petty problem via spherical harmonics.
- A positive answer to the Busemann-Petty problem in three dimensions
- Inversion formulas for the spherical Radon transform and the generalized cosine transform.
- Radon inversion on Grassmannians via Gårding-Gindikin fractional integrals
- Spherical harmonics
- Singular integrals
- Problems on convex bodies
- A note on a problem of H. Busemann and C. M. Petty concerning sections of symmetric convex bodies
- Convolutions, Transforms, and Convex Bodies
- Inequalities between projection functions of convex bodies
- On the Busemann‐Petty problem about convex, centrally symmetric bodies in
- Non-linear angle-sum relations for polyhedral cones and polytopes
- The existence of a centrally symmetric convex body with central sections that are unexpectedly small
- Intersection bodies, positive definite distributions, and the Busemann-Petty problem
- Intersection Bodies and the Busemann-Petty Problem
- Sections of Convex Bodies
- Radialpotenzintegrale zentralsymmetrischer Rotationskörper und Ungleichheitsaussagen Busemannscher Art.
- A functional analytic approach to intersection bodies
