Mean width inequalities for isotropic measures

DOI10.1007/s00209-011-0843-5zbMath1250.52003OpenAlexW2009450586MaRDI QIDQ415473

Ai-Jun Li, Gang Song Leng

Publication date: 8 May 2012

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

Full work available at URL: https://doi.org/10.1007/s00209-011-0843-5

zbMATH Keywords

Ball-Barthe inequalityisotropic measure\(\ell \)-normmean width inequality

Mathematics Subject Classification ID

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

Related Items (13)

Reverse Alexandrov–Fenchel inequalities for zonoids ⋮ Volume inequalities for \(L_0\)-Minkowski combination of convex bodies ⋮ Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds ⋮ The dual Loomis–Whitney inequality ⋮ Volume inequalities for sections and projections of Wulff shapes and their polars ⋮ Isomorphic versions of reverse isoperimetric inequalities ⋮ Mean width inequalities for symmetric Wulff shapes ⋮ Sections and projections of \(L_p\)-zonoids and their polars ⋮ An extremal property of \(p\)-mean width ⋮ Gaussian inequalities for Wulff shapes ⋮ Strengthened inequalities for the mean width and the ℓ‐norm ⋮ Volume inequalities for complex isotropic measures ⋮ The \(L_p\) Loomis-Whitney inequality

Cites Work

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• Extremal problems and isotropic positions of convex bodies
• A new ellipsoid associated with convex bodies
• Application of an idea of Voronoĭ to John type problems
• An arithmetic proof of John's ellipsoid theorem
• John's decomposition in the general case and applications
• Volume inequalities for subspaces of \(L_p\)
• Ellipsoids defined by Banach ideal norms
• Shadows of Convex Bodies
• Inégalités de Brascamp-Lieb et convexité
• $L_p$ John Ellipsoids
• Volume inequalities for isotropic measures
• John's theorem for an arbitrary pair of convex bodies
• John's decomposition of the identity in the non-convex case
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