Poincaré inequalities and moment maps

DOI10.5802/afst.1366zbMath1279.60036arXiv1104.2791OpenAlexW2963393941MaRDI QIDQ355210

Bo'az Klartag

Publication date: 24 July 2013

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.2791

zbMATH Keywords

convex bodiesmoment mapPoincaré inequalitiesregularity at infinitylog-concave functions\(l_p\) normdual Bochner formula

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Inequalities and extremum problems involving convexity in convex geometry (52A40)

Related Items (15)

Hessian metrics, \(CD(K, N)\)-spaces, and optimal transportation of log-concave measures ⋮ A proof of the Caffarelli contraction theorem via entropic regularization ⋮ A variational approach to some transport inequalities ⋮ On the Poincaré Constant of Log-Concave Measures ⋮ Remarks on curvature in the transportation metric ⋮ Large deviations, moderate deviations, and the KLS conjecture ⋮ Riemannian metrics on convex sets with applications to Poincaré and log-Sobolev inequalities ⋮ Riemannian metrics on \(\mathbb{R}^n\) and Sobolev-type inequalities ⋮ The Variance Conjecture on Some Polytopes ⋮ Brascamp-Lieb-type inequalities on weighted Riemannian manifolds with boundary ⋮ Extremal Kähler-Einstein metric for two-dimensional convex bodies ⋮ Remarks on the Central Limit Theorem for Non-convex Bodies ⋮ Logarithmically-Concave Moment Measures I ⋮ Moment measures ⋮ Relaxing the Gaussian assumption in shrinkage and SURE in high dimension

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hessian metrics, \(CD(K, N)\)-spaces, and optimal transportation of log-concave measures
• Sudakov's typical marginals, random linear functionals and a conditional central limit theorem
• A Berry-Esseen type inequality for convex bodies with an unconditional basis
• Functional analysis, Sobolev spaces and partial differential equations
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• Kaehler structures on toric varieties
• Elliptic partial differential equations of second order
• Kähler metrics on toric orbifolds.
• Harmonic maps of V-manifolds
• On concentration of distributions of random weighted sums
• Asymptotics of graphical projection pursuit
• A central limit theorem for convex sets
• Spherical harmonics
• Approximately gaussian marginals and the hyperplane conjecture
• Uniqueness theorems on conformal deformation of metrics, sobolev inequalities, and an eigenvalue estimate
• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• The central limit problem for convex bodies
• Invariances in variance estimates
• Riemannian Geometry
• Unified Poincaré and Hardy inequalities with sharp constants for convex domains
• Lectures on symplectic geometry

This page was built for publication: Poincaré inequalities and moment maps