Sharp inequalities related to the functional \(U_j\) and some applications

DOI10.1007/s10711-020-00573-zzbMath1467.52014OpenAlexW3096935484MaRDI QIDQ2039258

Si-Tao Zhang, Ai-Jun Li

Publication date: 2 July 2021

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

Full work available at URL: https://doi.org/10.1007/s10711-020-00573-z

zbMATH Keywords

isotropic measurecone-volume measureSchneider's projection problemparameterized functional \(U_j\)

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40)

Cites Work

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• The cone volume measure of antipodal points
• The log-Brunn-Minkowski inequality
• The dual Minkowski problem for negative indices
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Extremum problems for the cone volume functional of convex polytopes
• Reverse inequalities for zonoids and their application
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Cone-volume measure and stability
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Centroid surfaces
• Projection problems for symmetric polytopes
• Cone-volume measure of general centered convex bodies
• A volume inequality for polar bodies
• General affine surface areas
• On a reverse form of the Brascamp-Lieb inequality
• A new ellipsoid associated with convex bodies
• Existence of solutions to the even dual Minkowski problem
• On the \(L_p\) dual Minkowski problem
• The \(L_p\)-Aleksandrov problem for \(L_p\)-integral curvature
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Volume inequalities for asymmetric Wulff shapes
• The logarithmic Minkowski problem for polytopes
• Affine images of isotropic measures
• On LYZ's conjecture for the \(U\)-functional
• Cone-volume measures of polytopes
• Volume inequalities for subspaces of \(L_p\)
• The centro-affine Minkowski problem for polytopes
• A new affine invariant for polytopes and Schneider’s projection problem
• On the Discrete Logarithmic Minkowski Problem
• Centro-Affine Invariants for Smooth Convex Bodies
• Volume Ratios and a Reverse Isoperimetric Inequality
• Centroid Bodies and Dual Mixed Volumes
• Random hyperplanes meeting a convex body
• Shadows of Convex Bodies
• Volumes of projection bodies
• On the Loomis-Whitney Inequality for Isotropic Measures
• The logarithmic Minkowski problem
• Convex Bodies The Brunn-MinkowskiTheory
• Volume inequalities for isotropic measures
• $p$-Means of Convex Bodies.

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