Cone-volume measure of general centered convex bodies

DOI10.1016/j.aim.2015.09.021zbMath1334.52003OpenAlexW1832993423MaRDI QIDQ890138

Martin Henk, Károly jun. Böröczky

Publication date: 9 November 2015

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

Full work available at URL: https://doi.org/10.1016/j.aim.2015.09.021

zbMATH Keywords

polytopecentroid\(L_p\)-Minkowski problemcone-volume measurecentro-affine inequalitiessubspace concentration conditionU-functional\(\log\)-Minkowski problem

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

The logarithmic John ellipsoid, The \(L_{p}\)-Minkowski problem for \(-n < p < 1\), On the \(L_p\) dual Minkowski problem, A Brunn-Minkowski theory for coconvex sets of finite volume, A New Affine Invariant Geometric Functional for Polytopes and Its Associated Affine Isoperimetric Inequalities, Strengthened volume inequalities for $L_p$ zonoids of even isotropic measures, On the \(L^p\) Aleksandrov problem for negative \(p\), The discrete logarithmic Minkowski problem for \(q\)-capacity, Necessary subspace concentration conditions for the even dual Minkowski problem, Log-Brunn-Minkowski inequality under symmetry, The log-Minkowski inequality of curvature entropy, Extremal arrangements of points in the sphere for weighted cone-volume functionals, Notes on the log-Brunn-Minkowski inequality, Affine subspace concentration conditions for centered polytopes, On subspace concentration for dual curvature measures, Sharp affine isoperimetric inequalities for the Minkowski first mixed volume, On the planar Gaussian-Minkowski problem, The \(L_p\) John ellipsoids for negative indices, Some logarithmic Minkowski inequalities for nonsymmetric convex bodies, Subspace concentration of mixed volume measures, \(L_{p}\) dual curvature measures, Continuity of the solution to the dual Minkowski problem for negative indices, The logarithmic Minkowski problem for non-symmetric measures, The dual Minkowski problem for negative indices, On the \(L_{p}\) Monge-Ampère equation, The Minkowski problem in Gaussian probability space, Cone-volume measure and stability, Sharp inequalities related to the functional \(U_j\) and some applications, A new approach to the Minkowski first mixed volume and the LYZ conjecture, Stable solution of the Logarithmic Minkowski problem in the case of hyperplane symmetries, Sharp affine isoperimetric inequalities for the volume decomposition functionals of polytopes, The log-Brunn-Minkowski inequality in ℝ³, The 𝐿_{𝑝} Aleksandrov problem for origin-symmetric polytopes, Continuity of the solution to the even logarithmic Minkowski problem in the plane, Uniform distributions and random variate generation over generalized \(l_p\) balls and spheres, The \(L _p\) capacitary Minkowski problem for polytopes, The dual Minkowski problem for symmetric convex bodies, The L_p Minkowski problem for the electrostatic p-capacity for $p\ge n$, Uniqueness of solutions to the logarithmic Minkowski problem in \(\mathbb{R}^3\), On LYZ's conjecture for the \(U\)-functional, The planar \(L_{p}\)-Minkowski problem for \(0<p<1\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The cone volume measure of antipodal points
• The log-Brunn-Minkowski inequality
• Extremum problems for the cone volume functional of convex polytopes
• Interpolating thin-shell and sharp large-deviation estimates for isotropic log-concave measures
• A Berry-Esseen type inequality for convex bodies with an unconditional basis
• Projection problems for symmetric polytopes
• On nearly radial marginals of high-dimensional probability measures
• General affine surface areas
• Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities
• On a reverse form of the Brascamp-Lieb inequality
• On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
• The discrete planar \(L_0\)-Minkowski problem
• A probabilistic approach to the geometry of the \(\ell^n_p\)-ball
• Projecting the surface measure of the sphere of \({\ell}_p^n\)
• Isoperimetric problems for convex bodies and a localization lemma
• The logarithmic Minkowski problem for polytopes
• Affine images of isotropic measures
• Cone-volume measures of polytopes
• The Brascamp-Lieb inequalities: Finiteness, structure and extremals
• Volume inequalities for subspaces of \(L_p\)
• The centro-affine Minkowski problem for polytopes
• A new affine invariant for polytopes and Schneider’s projection problem
• Centro-Affine Invariants for Smooth Convex Bodies
• Relative entropy of cone measures and L _p centroid bodies
• The Centro-Affine Hadwiger Theorem
• Ehrhart Polynomials and Successive Minima
• The surface measure and cone measure on the sphere of ℓ_{𝑝}ⁿ
• Volume Ratios and a Reverse Isoperimetric Inequality
• Logarithmically concave functions and sections of convex sets in $R^{n}$
• The Brunn-Minkowski inequality
• $L_p$ John Ellipsoids
• Invariances in variance estimates
• The logarithmic Minkowski problem
• Convex and Discrete Geometry
• Volume inequalities for isotropic measures
• The Gauss-Green Theorem