Busemann-Petty Type Problem for the General $L_p$-Centroid Bodies

DOI10.4208/ata.OA-2021-0030OpenAlexW4322756990MaRDI QIDQ5882450

Wei-Dong Wang

Publication date: 16 March 2023

Published in: Analysis in Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/ata.oa-2021-0030

zbMATH Keywords

Busemann-Petty problem\(L_p\)-centroid bodygeneral \(L_p\)-centroid bodyaffirmation formnegation form

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) Mixed volumes and related topics in convex geometry (52A39) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (1)

$q$-Quermassintegral forms of the $L_p$-Busemann–Petty centroid inequality

Cites Work

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• Shephard type problems for general \(L_{p}\)-centroid bodies
• Extremum of geometric functionals involving general \(L_{p}\)-projection bodies
• A general \(L_p\)-version of Petty's affine projection inequality
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Centroid surfaces
• General \(L_{p}\) affine isoperimetric inequalities
• On some affine isoperimetric inequalities
• Blaschke-Santaló inequalities
• The \(L^p\)-Busemann-Petty centroid inequality
• \(L_ p\) affine isoperimetric inequalities.
• Shephard type problems for general \(L_p\)-projection bodies
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• The Petty projection inequality for \(L_p\)-mixed projection bodies
• General \(L_{p}\)-harmonic Blaschke bodies
• Volume extremals of general L_p-centroid bodies
• A type of monotonicity on the L_p centroid body and L_p projection body
• Centroid Bodies and Dual Mixed Volumes
• Convolutions, Transforms, and Convex Bodies
• Centered Bodies and Dual Mixed Volumes
• On the reverse L ^p –busemann–petty centroid inequality
• Shephard type problems for L_p-centroid bodies
• Some inequalities on general L_p-centroid bodies
• Convex Bodies The Brunn-MinkowskiTheory
• Minkowski valuations

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