Volume inequalities for complex isotropic measures

DOI10.1007/s10711-014-9996-9zbMath1321.52006OpenAlexW2123253959MaRDI QIDQ2516437

Qingzhong Huang, Bin-Wu He

Publication date: 3 August 2015

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-014-9996-9

zbMATH Keywords

sine transform\(L_p\)-cosine transformcomplex isotropic measure

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

Isomorphic versions of reverse isoperimetric inequalities ⋮ Inequalities for complex centroid bodies ⋮ The complex L_p Loomis-Whitney inequality ⋮ Mixed complex brightness integrals

Cites Work

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• The unconditional case of the complex \(S\)-inequality
• Shadow systems of asymmetric \(L_p\) zonotopes
• Mean width inequalities for isotropic measures
• Projection bodies in complex vector spaces
• Stability of volume comparison for complex convex bodies
• Gaussian measures of dilations of convex rotationally symmetric sets in \(C^n\)
• Hermitian integral geometry
• Reverse inequalities for zonoids and their application
• Difference bodies in complex vector spaces
• Gaussian kernels have only Gaussian maximizers
• A volume inequality for polar bodies
• The complex Busemann-Petty problem for arbitrary measures
• Optimisers for the Brascamp-Lieb inequality
• The modified complex Busemann-Petty problem on sections of convex bodies
• On a reverse form of the Brascamp-Lieb inequality
• Best constants in Young's inequality, its converse, and its generalization to more than three functions
• An extremal property of the mean width of the simplex
• Extremal problems and isotropic positions of convex bodies
• The Gauss-Bonnet theorem and Crofton-type formulas in complex space forms
• The Busemann theorem for complex \(p\)-convex bodies
• Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations.
• Volume inequalities for asymmetric Wulff shapes
• The complex Busemann-Petty problem on sections of convex bodies
• Volume inequalities for subspaces of \(L_p\)
• Structure of the unitary valuation algebra
• Polydisc slicing in $ℂ^n$
• Complex intersection bodies
• The Sine Transform of Isotropic Measures
• Volume Ratios and a Reverse Isoperimetric Inequality
• Shadows of Convex Bodies
• Isotropic surface area measures
• Extremal sections of complex l_p-balls, 0 < p ≤2
• Minkowski Valuations in a 2-Dimensional Complex Vector Space
• Minimal volume of slabs in the complex cube
• Volume inequalities for isotropic measures
• Matrix theory. Basic results and techniques
• John's decomposition of the identity in the non-convex case