Equivalence of the local and global versions of the \(L^p\)-Brunn-Minkowski inequality

DOI10.1016/j.jfa.2021.108956zbMath1461.52010arXiv1909.03729OpenAlexW3133322497MaRDI QIDQ2662514

Eli Putterman

Publication date: 14 April 2021

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.03729

zbMATH Keywords

log-Brunn-Minkowski inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39)

Related Items (12)

The logarithmic Minkowski inequality for cylinders ⋮ On Discrete LOG-Brunn--Minkowski Type Inequalities ⋮ Local 𝐿^{𝑝}-Brunn–Minkowski inequalities for 𝑝<1 ⋮ Log-Brunn-Minkowski inequality under symmetry ⋮ Notes on the log-Brunn-Minkowski inequality ⋮ On \(p\)-Brunn-Minkowski inequalities for intrinsic volumes, with \(0\le p<1\) ⋮ On the planar Gaussian-Minkowski problem ⋮ Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting) ⋮ Subspace concentration of mixed volume measures ⋮ On the \(L_p\)-Brunn-Minkowski and dimensional Brunn-Minkowski conjectures for log-concave measures ⋮ Stable solution of the Logarithmic Minkowski problem in the case of hyperplane symmetries ⋮ The \(L_p\)-Gaussian Minkowski problem

Cites Work

• The log-Brunn-Minkowski inequality
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Affine Moser-Trudinger and Morrey-Sobolev inequalities
• Santaló's inequality on \(\mathbb{C}^n\) by complex interpolation
• Sharp affine \(L_ p\) Sobolev inequalities.
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• The logarithmic Minkowski problem for polytopes
• The \(L_p\) Minkowski problem for polytopes for \(0 < p < 1\)
• On the stability of Brunn-Minkowski type inequalities
• The centro-affine Minkowski problem for polytopes
• A new proof of the log-Brunn-Minkowski inequality
• Remarks on the conjectured log-Brunn-Minkowski inequality
• MORE ON LOGARITHMIC SUMS OF CONVEX BODIES
• The Brunn-Minkowski inequality
• The logarithmic Minkowski problem for non-symmetric measures
• On the $L_{p}$-Minkowski problem
• The logarithmic Minkowski problem
• 6. A note on the quantitative local version of the log-Brunn–Minkowski inequality
• Convex Bodies The Brunn-MinkowskiTheory
• Optimal Sobolev norms and the Lp Minkowski problem
• $p$-Means of Convex Bodies.

This page was built for publication: Equivalence of the local and global versions of the \(L^p\)-Brunn-Minkowski inequality