The complex L_p Loomis-Whitney inequality

DOI10.7153/mia-2018-21-27zbMath1395.52006OpenAlexW2793504005MaRDI QIDQ4634656

Ai-Jun Li, Qingzhong Huang, Wei Wang

Publication date: 11 April 2018

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

Full work available at URL: https://doi.org/10.7153/mia-2018-21-27

zbMATH Keywords

complex \( L_p\) projection bodiescomplex \( L_p\) zonoidcomplex \(L_p\) Loomis-Whitney inequalitycomplex cross measurecomplex isotropic measuresgeneralized \(\ell_p ({\mathbb C}^n) \)-balls

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 (3)

Inequalities for complex centroid bodies ⋮ On Complex L_p affine isoperimetric inequalities ⋮ Mixed complex brightness integrals

Cites Work

• The \(L_p\) Loomis-Whitney inequality
• The unconditional case of the complex \(S\)-inequality
• Projections, entropy and sumsets
• Projection bodies in complex vector spaces
• Stability of volume comparison for complex convex bodies
• Hermitian integral geometry
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Difference bodies in complex vector spaces
• Estimates of Loomis-Whitney type for intrinsic volumes
• Aleksandrov-Fenchel inequalities for unitary valuations of degree 2 and 3
• On the multilinear restriction and Kakeya conjectures
• The affine Sobolev inequality.
• The Gauss-Bonnet theorem and Crofton-type formulas in complex space forms
• Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations.
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Integral geometry of complex space forms
• The complex Busemann-Petty problem on sections of convex bodies
• Volume inequalities for complex isotropic measures
• A nonlinear generalisation of the Loomis-Whitney inequality and applications
• Reverse and dual Loomis-Whitney-type inequalities
• Complex intersection bodies
• AN EXTENDED LOOMIS–WHITNEY INEQUALITY FOR POSITIVE DOUBLE JOHN BASES
• The dual Loomis–Whitney inequality
• Estimating the Sizes of Convex Bodies from Projections
• Shadows of Convex Bodies
• On the Loomis-Whitney Inequality for Isotropic Measures
• $L_p$ John Ellipsoids
• Projections of Bodies and Hereditary Properties of Hypergraphs
• Minkowski Valuations in a 2-Dimensional Complex Vector Space
• How do difference bodies in complex vector spaces look like? A geometrical approach
• Convex Bodies The Brunn-MinkowskiTheory
• An inequality related to the isoperimetric inequality

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