Inequalities for mixed \(p\)-affine surface area

DOI10.1007/s00208-009-0453-2zbMath1192.52013arXiv0812.4550OpenAlexW3103847484MaRDI QIDQ971904

Deping Ye, Elisabeth M. Werner

Publication date: 17 May 2010

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.4550

zbMATH Keywords

affine isoperimetric inequalities\(L_p\)-affine surface areaAleksandrov-Fenchel type inequalitiesBlaschke-Santaló type inequalitiesillumination surface bodymixed \(p\)-affine surface area

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Affine differential geometry (53A15)

Related Items (35)

Dual Orlicz-Brunn-Minkowski theory: dual Orlicz \(L_{\phi}\) affine and geominimal surface areas ⋮ \((p,q)\)-mixed geominimal surface area and \((p,q)\)-mixed affine surface area ⋮ The Centro-Affine Hadwiger Theorem ⋮ \(L_p\)-curvature measures and \(L_{p, q}\)-mixed volumes ⋮ Floating functions ⋮ Ulam floating functions ⋮ \(L_p\)-Steiner quermassintegrals ⋮ Volume extremals of general L_p-centroid bodies ⋮ A generalized rotationally symmetric case of the centroaffine Minkowski problem ⋮ Rényi divergence and \(L_p\)-affine surface area for convex bodies ⋮ New affine measures of symmetry for convex bodies ⋮ On the Orlicz Minkowski problem for polytopes ⋮ Divergence for \(s\)-concave and log concave functions ⋮ \(L_p\) mixed geominimal surface area ⋮ On mixed quermassintegral for log-concave functions ⋮ \(L_p\)-dual mixed affine surface areas ⋮ The mixed L_p affine surface areas for functions ⋮ Extremal general affine surface areas ⋮ Some inequalities for the L p -mixed quermassintegrals ⋮ \(L_{p}\) dual curvature measures ⋮ The \((q,{\phi})\)-dual Orlicz mixed affine surface areas ⋮ Relative entropies for convex bodies ⋮ Mixedf-divergence and inequalities for log-concave functions ⋮ Inequalities for the radial p-th mean bodies ⋮ Dual mixed Orlicz-Brunn-Minkowski inequality and dual Orlicz mixed quermassintegrals ⋮ The even Orlicz Minkowski problem ⋮ A Steiner formula in the \(L_p\) Brunn Minkowski theory ⋮ Some \(\log\)-Minkowski inequalities for \(L_p\)-mixed affine surface area ⋮ Optimal problem for mixed \(p\)-capacities ⋮ Some inequalities for the L_p-curvature images ⋮ Cyclic Brunn-Minkowski inequalities forp-affine surface area ⋮ Some inequalities for the (p, q)-mixed affine surface areas ⋮ Separation bodies: a conceptual dual to floating bodies ⋮ New Orlicz affine isoperimetric inequalities ⋮ Shephard type problems for general \(L_{p}\)-centroid bodies

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