Local 𝐿^{𝑝}-Brunn–Minkowski inequalities for 𝑝<1

DOI10.1090/memo/1360zbMath1502.52002arXiv1711.01089OpenAlexW4293085101MaRDI QIDQ5097129

Alexander V. Kolesnikov, Emanuel Milman

Publication date: 19 August 2022

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.01089

zbMATH Keywords

Poincaré inequalityconvex bodiesAleksandrov body\(L^p\)-Brunn-Minkowski theoryHilbert-Brunn-Minkowski operatorisoperimetric stability estimateslocal uniqueness in \(L^p\)-Minkowski problem

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Research exposition (monographs, survey articles) pertaining to convex and discrete geometry (52-02) Asymptotic theory of convex bodies (52A23)

Related Items (19)

The logarithmic Minkowski inequality for cylinders ⋮ On the stability of the \(L_p\)-curvature ⋮ On Discrete LOG-Brunn--Minkowski Type Inequalities ⋮ Log-Brunn-Minkowski inequality under symmetry ⋮ Improved log-concavity for rotationally invariant measures of symmetric convex sets ⋮ On the \(L_p\) Gaussian Minkowski problem ⋮ On mixed Hodge–Riemann relations for translation-invariant valuations and Aleksandrov–Fenchel inequalities ⋮ A Chapter About Asymptotic Geometric Analysis: Isomorphic Position of Centrally Symmetric Convex Bodies ⋮ Notes on the log-Brunn-Minkowski inequality ⋮ On \(p\)-Brunn-Minkowski inequalities for intrinsic volumes, with \(0\le p<1\) ⋮ Uniqueness of solutions to a class of mixed Hessian quotient type equations ⋮ A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures ⋮ On the polar Orlicz Minkowski type problem for the general mixed \(\mathfrak{p}\)-capacity ⋮ Uniqueness of solutions to a class of isotropic curvature problems ⋮ On the planar Gaussian-Minkowski problem ⋮ On the uniqueness of solutions to the isotropic \(L_p\) dual Minkowski problem ⋮ Subspace concentration of mixed volume measures ⋮ Uniqueness of solutions to the logarithmic Minkowski problem in \(\mathbb{R}^3\) ⋮ Affine invariant maps for log-concave functions

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