New \(L_p\) affine isoperimetric inequalities

DOI10.1016/j.aim.2008.02.002zbMath1155.52002arXiv0711.1867OpenAlexW2043182033MaRDI QIDQ2427569

Elisabeth M. Werner, Deping Ye

Publication date: 13 May 2008

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

Full work available at URL: https://arxiv.org/abs/0711.1867

zbMATH Keywords

affine surface area\(L_p\)-Brunn-Minkowski theory

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Affine differential geometry (53A15)

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

Curvature functionals on convex bodies ⋮ Ulam floating functions ⋮ \(L_p\)-Steiner quermassintegrals ⋮ The \(L_p\) John ellipsoids for negative indices ⋮ \(L_p\) Blaschke-Santaló and Petty projection inequalities in Gaussian space ⋮ Orlicz version of mixed moment tensors ⋮ The characteristic properties of the minimal \(L_p\)-mean width ⋮ Some inequalities for \((p,q)\)-mixed volume ⋮ Dual Orlicz affine surface area ⋮ The logarithmic John ellipsoid ⋮ Orlicz-Aleksandrov-Fenchel inequality for Orlicz multiple mixed volumes ⋮ The optimal problems for torsional rigidity ⋮ Isoperimetric and Brunn-Minkowski inequalities for the \((p, q)\)-mixed geominimal surface areas ⋮ Floating bodies and approximation of convex bodies by polytopes ⋮ Dual Orlicz-Brunn-Minkowski theory: dual Orlicz \(L_{\phi}\) affine and geominimal surface areas ⋮ The spherical convex floating body ⋮ \((p,q)\)-mixed geominimal surface area and \((p,q)\)-mixed affine surface area ⋮ The Centro-Affine Hadwiger Theorem ⋮ The LYZ centroid conjecture for star bodies ⋮ Affine Orlicz Pólya-Szegő principle for log-concave functions ⋮ \(L_p\)-curvature measures and \(L_{p, q}\)-mixed volumes ⋮ The minimal Orlicz surface area ⋮ Extremum problems for the cone volume functional of convex polytopes ⋮ Constrained convex bodies with extremal affine surface areas ⋮ Shadow systems of asymmetric \(L_p\) zonotopes ⋮ The Orlicz-Lorentz centroid inequality for star bodies* ⋮ Orlicz-John ellipsoids ⋮ The Brunn-Minkowski-Firey inequality for nonconvex sets ⋮ The Orlicz centroid inequality for star bodies ⋮ On the polar Orlicz-Minkowski problems and the p-capacitary Orlicz-Petty bodies ⋮ Rényi divergence and \(L_p\)-affine surface area for convex bodies ⋮ The \((\varphi, \psi)\) Orlicz mixed Petty bodies ⋮ Dual Orlicz Mixed Quermassintegral ⋮ The generalization of Minkowski problems for polytopes ⋮ A remark on rotationally symmetric solutions to the centroaffine Minkowski problem ⋮ On the discrete Orlicz electrostatic \(q\)-capacitary Minkowski problem ⋮ New affine measures of symmetry for convex bodies ⋮ L_p dual mixed geominimal surface areas for multiple star bodies ⋮ On the Orlicz Minkowski problem for polytopes ⋮ The log-Brunn-Minkowski inequality ⋮ Divergence for \(s\)-concave and log concave functions ⋮ \(L_p\) mixed geominimal surface area ⋮ On mixed quermassintegral for log-concave functions ⋮ Stability in the \(L_p\) Shephard problem ⋮ On the stability of the \(p\)-affine isoperimetric inequality ⋮ \(L_p\)-dual mixed affine surface areas ⋮ The mixed L_p affine surface areas for functions ⋮ A new proof of the Orlicz Busemann-Petty centroid inequality ⋮ L_p-DUAL MIXED GEOMINIMAL SURFACE AREA ⋮ \((p, q)\)-John ellipsoids ⋮ Extremal general affine surface areas ⋮ $\mathrm {SL}(n)$-contravariant $L_p$-Minkowski valuations ⋮ Fractional perimeters on the sphere ⋮ Sections and projections of \(L_p\)-zonoids and their polars ⋮ \(L_p\)-dual affine surface area ⋮ Volume inequalities for asymmetric Orlicz zonotopes ⋮ Approximation of smooth convex bodies by random polytopes ⋮ The \((q,{\phi})\)-dual Orlicz mixed affine surface areas ⋮ SL(n)-covariantL_p-Minkowski valuations ⋮ On isoperimetric inequalities in Minkowski spaces ⋮ Halfspace depth and floating body ⋮ Relative entropies for convex bodies ⋮ Mixedf-divergence and inequalities for log-concave functions ⋮ Inequalities for the radial p-th mean bodies ⋮ Inequalities for mixed \(p\)-affine surface area ⋮ Dual mixed Orlicz-Brunn-Minkowski inequality and dual Orlicz mixed quermassintegrals ⋮ Orlicz mixed quermassintegrals ⋮ General affine surface areas ⋮ The even Orlicz Minkowski problem ⋮ A Steiner formula in the \(L_p\) Brunn Minkowski theory ⋮ Orlicz extensions of Brunn-Minkowski theory ⋮ Unnamed Item ⋮ Flag numbers and floating bodies ⋮ Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory ⋮ Dual Orlicz geominimal surface area ⋮ Surface area deviation between smooth convex bodies and polytopes ⋮ Some \(\log\)-Minkowski inequalities for \(L_p\)-mixed affine surface area ⋮ General \((p,q)\)-mixed projection bodies ⋮ Ulam floating bodies ⋮ Some inequalities for the L_p-curvature images ⋮ Dual Orlicz mixed geominimal surface area ⋮ ISOPERIMETRIC INEQUALITIES FOR L_p GEOMINIMAL SURFACE AREA ⋮ A new proof of the Orlicz-Lorentz centroid inequality ⋮ Unnamed Item ⋮ Orlicz affine isoperimetric inequalities for star bodies ⋮ Blaschke-Santaló inequality for many functions and geodesic barycenters of measures ⋮ Cyclic Brunn-Minkowski inequalities forp-affine surface area ⋮ New sine ellipsoids and related volume inequalities ⋮ Extremal problems for \(L_p\) surface areas and John ellipsoids ⋮ On the convolution bodies of \(L_p\)-addition ⋮ The (p, q)-mixed geominimal surface areas ⋮ The general dual-polar Orlicz-Minkowski problem ⋮ On mixed \(L_{p}\) John ellipsoids ⋮ Some inequalities for the (p, q)-mixed affine surface areas ⋮ The Orlicz–Minkowski problem for measure in ℝn and Orlicz geominimal measures ⋮ Orlicz projection bodies ⋮ Separation bodies: a conceptual dual to floating bodies ⋮ Unnamed Item ⋮ New Orlicz affine isoperimetric inequalities ⋮ The minimal Orlicz mean width of convex bodies

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Invariant valuations on star-shaped sets
• Extended affine surface area
• From the Mahler conjecture to Gauss linking integrals
• Continuous rotation invariant valuations on convex sets
• On affine plane curve evolution
• Ellipsoids and matrix-valued valuations
• 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
• \(L_ p\) affine isoperimetric inequalities.
• Sharp affine \(L_ p\) Sobolev inequalities.
• The distribution function of the convolution square of a convex symmetric body in \({\mathbb{R}{}}^ n\)
• Gauss curvature flow: The fate of the rolling stones
• New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
• 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
• Contraction of convex hypersurfaces by their affine normal
• Curvature relations and affine surface area for a general convex body and its polar
• A characterization of affine surface area
• \(L_p\) Minkowski problem with not necessarily positive data
• A stability result for mean width of \(L_{p}\)-centroid bodies
• A central limit theorem for convex sets
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• The convex floating body.
• The Santaló-regions of a convex body
• Illumination bodies and affine surface area
• Affine inequalities and radial mean bodies
• The affine Plateau problem
• Approximation of the Euclidean ball by polytopes
• Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture

This page was built for publication: New \(L_p\) affine isoperimetric inequalities