The even Orlicz Minkowski problem

DOI10.1016/j.aim.2010.02.006zbMath1198.52003OpenAlexW2112297948MaRDI QIDQ984880

Christoph Haberl, Erwin Lutwak, Deane Yang, Gaoyong Zhang

Publication date: 20 July 2010

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

Full work available at URL: https://doi.org/10.1016/j.aim.2010.02.006

zbMATH Keywords

Orlicz normsupport functionMinkowski problemAleksandrov bodyPetty projection inequality\(L_p\) Minkowski problemsurface area measure

Mathematics Subject Classification ID

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

Related Items (only showing first 100 items - show all)

Orlicz version of mixed moment tensors ⋮ Existence of solution for Lp-Minkowski problem of 0 < p < 1 with measures in ℝn ⋮ Orlicz-Legendre ellipsoids ⋮ Successive radii and Orlicz Minkowski sum ⋮ Volume inequalities for \(L_0\)-Minkowski combination of convex bodies ⋮ The Centro-Affine Hadwiger Theorem ⋮ Orlicz-Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms ⋮ On the uniqueness and continuity of the dual area measure ⋮ Affine Orlicz Pólya-Szegő principle for log-concave functions ⋮ The minimal Orlicz surface area ⋮ 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 discrete logarithmic Minkowski problem for \(q\)-capacity ⋮ The Orlicz Minkowski Problem for general measures ⋮ Local 𝐿^{𝑝}-Brunn–Minkowski inequalities for 𝑝<1 ⋮ Deforming a convex hypersurface by anisotropic curvature flows ⋮ On the existence of solutions to the Orlicz Aleksandrov problem ⋮ On the \(L_p\) Gaussian Minkowski problem ⋮ Extremal arrangements of points in the sphere for weighted cone-volume functionals ⋮ Orlicz inequalities for radial Blaschke-Minkowski homomorphisms ⋮ Weighted Minkowski’s existence theorem and projection bodies ⋮ Existence of non-symmetric solutions to the Gaussian Minkowski problem ⋮ Flow by 𝜎_{𝑘} curvature to the Orlicz Christoffel-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 ⋮ \(L_p\)-Steiner quermassintegrals ⋮ The Orlicz Brunn-Minkowski inequality for the first eigenvalue of \(p\)-Laplacian ⋮ Convex hypersurfaces with prescribed Musielak-Orlicz-Gauss image measure ⋮ The \(L_p\) chord Minkowski problem ⋮ On the polar Orlicz Minkowski type problem for the general mixed \(\mathfrak{p}\)-capacity ⋮ On the planar Gaussian-Minkowski problem ⋮ A flow to the Orlicz-Minkowski-type problem of \(\mathfrak{p}\)-capacity ⋮ The \(L_p\) John ellipsoids for negative indices ⋮ The multiple radial Blaschke-Minkowski homomorphisms ⋮ The \((\varphi, \psi)\) Orlicz mixed Petty bodies ⋮ Dual Orlicz Mixed Quermassintegral ⋮ On the existence of solutions to the Orlicz-Minkowski problem for torsional rigidity ⋮ The minimal affine total variation on \(BV(\mathbb{R}^n)\) ⋮ The generalization of Minkowski problems for polytopes ⋮ The Orlicz Brunn-Minkowski inequality ⋮ A new proof of the Orlicz Busemann-Petty centroid inequality ⋮ A flow method for the dual Orlicz–Minkowski problem ⋮ The polar Orlicz-Brunn-Minkowski inequalities ⋮ Log-concavity properties of Minkowski valuations ⋮ Continuity of the solution to the even Lp Minkowski problem for 0 < p < 1 in the plane ⋮ Orlicz Version of Mixed Mean Dual Affifine Quermassintegrals ⋮ Continuity of the solution to the dual Minkowski problem for negative indices ⋮ On the discrete Orlicz Minkowski problem ⋮ The logarithmic Minkowski problem for non-symmetric measures ⋮ Relative entropies for convex bodies ⋮ The logarithmic Minkowski problem ⋮ The planar Busemann-Petty centroid inequality and its stability ⋮ Dual Orlicz geominimal surface area ⋮ Dual Orlicz mixed geominimal surface area ⋮ On Brunn-Minkowski type inequality ⋮ ISOPERIMETRIC INEQUALITIES FOR L_p GEOMINIMAL SURFACE AREA ⋮ Continuity of the solution to the $L_{p}$ Minkowski problem ⋮ Unnamed Item ⋮ Electrostatic capacity and measure of asymmetry ⋮ The Orlicz–Minkowski problem for measure in ℝn and Orlicz geominimal measures ⋮ Unnamed Item ⋮ The L_p Minkowski problem for the electrostatic p-capacity for $p\ge n$ ⋮ The minimal Orlicz mean width of convex bodies ⋮ Rogers and Shephard inequality for the Orlicz difference body ⋮ The planar Orlicz Minkowski problem in the \(L^1\)-sense ⋮ The planar \(L_{p}\)-Minkowski problem for \(0<p<1\) ⋮ On a non-homogeneous version of a problem of Firey ⋮ The dual \(\phi\)-Brunn-Minkowski inequality ⋮ The Orlicz Minkowski problem for the electrostatic \(\mathfrak{p}\)-capacity ⋮ LYZ ellipsoid and Petty projection body for log-concave functions ⋮ Mirror symmetric solutions to the centro-affine Minkowski problem ⋮ Orlicz-Aleksandrov-Fenchel inequality for Orlicz multiple mixed volumes ⋮ Orlicz mixed chord-integrals ⋮ The optimal problems for torsional rigidity ⋮ The \(L_{p}\)-Minkowski problem for \(-n < p < 1\) ⋮ General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. I ⋮ The \(L_p\) dual Minkowski problem about \(0 < p < 1\) and \(q > 0\) ⋮ On the reverse Orlicz Blaschke-Santaló inequality ⋮ A flow approach to the Musielak-Orlicz-Gauss image problem ⋮ On the \(L_p\) dual Minkowski problem ⋮ Existence and uniqueness of solutions to the Orlicz Aleksandrov problem ⋮ The discrete Orlicz-Minkowski problem for \(p\)-capacity ⋮ The Orlicz Brunn-Minkowski inequality for dual harmonic quermassintegrals ⋮ Smooth solutions to the Gauss image problem ⋮ The LYZ centroid conjecture for star bodies ⋮ The equality cases in Steiner's projection inequality ⋮ The \(L_p\) Gauss image problem ⋮ Orlicz mixed radial Blaschke-Minkowski homomorphisms ⋮ The \(L_p\)-Brunn-Minkowski inequality for \(p<1\) ⋮ The Hadamard variational formula and the Minkowski problem for \(p\)-capacity ⋮ Valuations on Orlicz spaces and \(L^\phi\)-star sets ⋮ Dual Orlicz-Brunn-Minkowski theory ⋮ An \(\text{SL}(n)\)-invariant mixed integral \(L_p\) affine surface area ⋮ Orlicz-John ellipsoids ⋮ On the dual Orlicz mixed volumes ⋮ The \(p\)-capacitary Orlicz-Hadamard variational formula and Orlicz-Minkowski problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• The Minkowski problem for polytopes
• An asymmetric affine Pólya-Szegő principle
• 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
• General \(L_{p}\) affine isoperimetric inequalities
• Convex and star-shaped sets associated with multivariate stable distributions. I: Moments and densities
• Orlicz projection bodies
• Affine Moser-Trudinger and Morrey-Sobolev inequalities
• Blaschke-Santaló inequalities
• 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
• The \(L^p\)-Busemann-Petty centroid inequality
• The discrete planar \(L_0\)-Minkowski problem
• The affine Sobolev inequality.
• \(L_ p\) affine isoperimetric inequalities.
• Sharp affine \(L_ p\) Sobolev inequalities.
• The Cramer-Rao inequality for star bodies
• Valuations on polytopes containing the origin in their interiors
• Projection bodies and valuations
• 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
• Small ball probability estimates, \(\psi_2\)-behavior and the hyperplane conjecture
• \(L_p\) Minkowski problem with not necessarily positive data
• A stability result for mean width of \(L_{p}\)-centroid bodies
• 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
• Intersection bodies and valuations
• A characterization of Lp intersection bodies
• Volume Inequalities forL_p‐Zonotopes
• A note on subgaussian estimates for linear functionals on convex bodies
• Star body valued valuations
• On the regularity of the solution of then-dimensional Minkowski problem
• The Brunn-Minkowski inequality
• 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
• Fourier transform and Firey projections of convex bodies
• On volume product inequalities for convex sets
• Convex and Discrete Geometry
• Small ball probability estimates for log-concave measures
• Volume inequalities for isotropic measures
• Minkowski valuations
• Optimal Sobolev norms and the Lp Minkowski problem
• Centroid bodies and comparison of volumes
• Hedgehogs and zonoids
• \(L_p\) intersection bodies

This page was built for publication: The even Orlicz Minkowski problem