The logarithmic Minkowski inequality for non-symmetric convex bodies

DOI10.1016/j.aam.2015.09.015zbMath1331.52014OpenAlexW2172758441MaRDI QIDQ900981

Alina Stancu

Publication date: 23 December 2015

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2015.09.015

zbMATH Keywords

log-Brunn-Minkowski inequalitycone-volume measurelog-Minkowski inequality\(L_0\)-Minkowski problem

Mathematics Subject Classification ID

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

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Cites Work

• Unnamed Item
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• Orlicz-John ellipsoids
• The log-Brunn-Minkowski inequality
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Cone-volume measure and stability
• Evolving plane curves by curvature in relative geometries
• Evolving plane curves by curvature in relative geometries. II
• Hadamard's inequality for \(r\)-convex functions
• On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
• Extremal problems and isotropic positions of convex bodies
• The discrete planar \(L_0\)-Minkowski problem
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• The logarithmic Minkowski problem for polytopes
• Cone-volume measures of polytopes
• The necessary condition for the discrete \(L_{0}\)-Minkowski problem in \({\mathbb{R}}^{2}\)
• The Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities
• Remarks on the conjectured log-Brunn-Minkowski inequality
• On the Discrete Logarithmic Minkowski Problem
• Relative entropy of cone measures and L _p centroid bodies
• Ehrhart Polynomials and Successive Minima
• Centroid Bodies and Dual Mixed Volumes
• The logarithmic Minkowski problem
• Elements of Information Theory

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