On L_p intersection mean ellipsoids and affine isoperimetric inequalities

DOI10.7153/mia-2021-24-75zbMath1489.52004OpenAlexW3211025912MaRDI QIDQ5030405

Fangwei Chen, Xin Cai

Publication date: 17 February 2022

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/mia-2021-24-75

zbMATH Keywords

Minkowski inequalitydual mixed volume\(L^p\) affine quermassintegral\(L^p\) intersection ellipsoid

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Cites Work

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• Orlicz-John ellipsoids
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Orlicz centroid bodies
• Orlicz projection bodies
• Intersection bodies and dual mixed volumes
• New affine inequalities and projection mean ellipsoids
• Sharp affine \(L_ p\) Sobolev inequalities.
• Moment-entropy inequalities.
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Isoperimetric inequalities and identities for \(k\)-dimensional cross-sections of convex bodies
• On mixed \(L_{p}\) John ellipsoids
• Affine isoperimetric inequalities for intersection mean ellipsoids
• On the \(L_{p}\) Minkowski problem for polytopes
• Orlicz-Legendre ellipsoids
• A new affine invariant for polytopes and Schneider’s projection problem
• $L_p$ John Ellipsoids
• Information-theoretic inequalities for contoured probability distributions
• Optimal Sobolev norms and the Lp Minkowski problem
• $p$-Means of Convex Bodies.

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