On the Orlicz Minkowski problem for polytopes

DOI10.1007/s00454-012-9434-4zbMath1255.52006OpenAlexW2093577407MaRDI QIDQ452005

Qingzhong Huang, Bin-Wu He

Publication date: 19 September 2012

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-012-9434-4

zbMATH Keywords

convex polytopeOrlicz norm\(L_p\) Minkowski problemeven Orlicz Minkowski problem

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Orlicz version of mixed moment tensors, The dual \(\phi\)-Brunn-Minkowski inequality, Existence of solution for Lp-Minkowski problem of 0 < p < 1 with measures in ℝn, Orlicz-Aleksandrov-Fenchel inequality for Orlicz multiple mixed volumes, Orlicz mixed chord-integrals, The \(L_{p}\)-Minkowski problem for \(-n < p < 1\), Successive radii and Orlicz Minkowski sum, Existence and uniqueness of solutions to the Orlicz Aleksandrov problem, Smooth solutions to the Gauss image problem, Orlicz-Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms, The \(L_p\) Gauss image problem, Orlicz mixed radial Blaschke-Minkowski homomorphisms, The dual Orlicz-Brunn-Minkowski inequality for concave functions, Orlicz-Lorentz centroid bodies, Dual Orlicz mixed geominimal surface areas, On a planar conformal curvature problem, The Orlicz Minkowski Problem for general measures, On the existence of solutions to the Orlicz Aleksandrov problem, On the \(L_p\) Gaussian Minkowski problem, Dual Orlicz-Brunn-Minkowski theory, Existence of non-symmetric solutions to the Gaussian Minkowski problem, A flow method to the Orlicz-Aleksandrov problem, The Orlicz Minkowski problem for cone-volume measure, On the polar Orlicz-Minkowski problems and the p-capacitary Orlicz-Petty bodies, On the general dual Orlicz-Minkowski problem, The Orlicz Brunn-Minkowski inequality for the first eigenvalue of \(p\)-Laplacian, A flow to the Orlicz-Minkowski-type problem of \(\mathfrak{p}\)-capacity, On the dual Orlicz mixed volumes, The multiple radial Blaschke-Minkowski homomorphisms, The \(p\)-capacitary Orlicz-Hadamard variational formula and Orlicz-Minkowski problems, Orlicz mean dual affine quermassintegrals, The generalization of Minkowski problems for polytopes, Existence of solutions to the Orlicz-Minkowski problem, The dual Orlicz-Minkowski problem, On the discrete Orlicz electrostatic \(q\)-capacitary Minkowski problem, The Orlicz Brunn-Minkowski inequality, An asymmetric Orlicz centroid inequality for probability measures, Mixed volumes and measures of asymmetry, Orlicz-Minkowski flows, A flow method for the dual Orlicz–Minkowski problem, Continuity of the solution to the even Lp Minkowski problem for 0 < p < 1 in the plane, Orlicz difference bodies, Extremal general affine surface areas, Orlicz dual mixed volumes, Orlicz Version of Mixed Mean Dual Affifine Quermassintegrals, On the discrete Orlicz Minkowski problem, Dual Orlicz mixed affine quermassintegrals, The \((q,{\phi})\)-dual Orlicz mixed affine surface areas, Orlicz log-Minkowski inequality, Orlicz metrics for convex bodies, Dual mixed Orlicz-Brunn-Minkowski inequality and dual Orlicz mixed quermassintegrals, A sharp Rogers-Shephard type inequality for Orlicz-difference body of planar convex bodies, Orlicz extensions of Brunn-Minkowski theory, General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. II, Orlicz dual affine quermassintegrals, Existence and uniqueness of solutions to Orlicz Minkowski problems involving \(0 < p < 1\), The Orlicz-Minkowski problem for polytopes, The Orlicz Minkowski problem involving \(0 < p < 1 \): from one constant to an infinite interval, On the discrete Orlicz Minkowski problem. II, The \(L_p\) electrostatic \(q\)-capacitary Minkowski problem for general measures, Unnamed Item, Electrostatic capacity and measure of asymmetry, Existence of smooth even solutions to the dual Orlicz-Minkowski problem, A Gauss curvature flow to the Orlicz-Minkowski problem for torsional rigidity, The general dual-polar Orlicz-Minkowski problem, On the Orlicz Minkowski problem for logarithmic capacity, The Orlicz-Minkowski problem for torsional rigidity, The Orlicz–Minkowski problem for measure in ℝn and Orlicz geominimal measures, A new proof of the Orlicz-Lorentz Busemann-Petty centroid inequality, The planar Orlicz Minkowski problem for \(p=0\) without even assumptions, The Orlicz version of the \(L_p\) Minkowski problem for \(- n < p < 0\), Unnamed Item, Volume inequalities for Orlicz mean bodies, Rogers and Shephard inequality for the Orlicz difference body, The planar Orlicz Minkowski problem in the \(L^1\)-sense

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• The Minkowski problem for polytopes
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Concentration of mass on isotropic convex bodies
• Concentration of mass on convex bodies
• Inequalities for mixed \(p\)-affine surface area
• Orlicz centroid bodies
• General affine surface areas
• The even Orlicz Minkowski problem
• General \(L_{p}\) affine isoperimetric inequalities
• Orlicz projection bodies
• Affine Moser-Trudinger and Morrey-Sobolev inequalities
• A Minkowski problem for electrostatic capacity
• Ellipsoids and matrix-valued valuations
• On solvability of two-dimensional \(L_{p}\)-Minkowski problem.
• On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
• On the \(p\)-affine surface area
• A new ellipsoid associated with convex bodies
• A logarithmic Gauss curvature flow and the Minkowski problem.
• The \(L^p\)-Busemann-Petty centroid inequality
• The discrete planar \(L_0\)-Minkowski problem
• \(L_ p\) affine isoperimetric inequalities.
• Sharp affine \(L_ p\) Sobolev inequalities.
• Surface bodies and \(p\)-affine surface area
• On the Christoffel-Minkowski problem of Firey's \(p\)-sum
• On the regularity of solutions to a generalization of the Minkowski problem
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• \(L_p\) Minkowski problem with not necessarily positive data
• Asymmetric affine \(L_p\) Sobolev inequalities
• New \(L_p\) affine isoperimetric inequalities
• The necessary condition for the discrete \(L_{0}\)-Minkowski problem in \({\mathbb{R}}^{2}\)
• On the \(L_{p}\) Minkowski problem for polytopes
• Volume inequalities for subspaces of \(L_p\)
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• Star body valued valuations
• On the ψ₂-behaviour of linear functionals on isotropic convex bodies
• $L_p$ John Ellipsoids
• On the $L_{p}$-Minkowski problem
• On the reverse L ^p –busemann–petty centroid inequality
• Remarks on the 2-Dimensional L_p-Minkowski Problem
• Convex and Discrete Geometry
• Volume inequalities for isotropic measures
• Minkowski valuations
• Optimal Sobolev norms and the Lp Minkowski problem
• Numerical solution of the Minkowski problem
• \(L_p\) intersection bodies