Rigidity and stability of Caffarelli's log-concave perturbation theorem

DOI10.1016/j.na.2016.10.006zbMath1359.60050arXiv1605.09702OpenAlexW2962875168WikidataQ112631929 ScholiaQ112631929MaRDI QIDQ515696

Alessio Figalli, Guido De Philippis

Publication date: 16 March 2017

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.09702

zbMATH Keywords

optimal transportlog concave measures

Mathematics Subject Classification ID

Gaussian processes (60G15) Probability measures on topological spaces (60B05) Variational methods for second-order elliptic equations (35J20)

Related Items (10)

Stability of eigenvalues and observable diameter in RCD\((1, \infty)\) spaces ⋮ Stability of the Bakry-Émery theorem on \(\mathbb{R}^n\) ⋮ A proof of the Caffarelli contraction theorem via entropic regularization ⋮ Self-improvement of the Bakry-Emery criterion for Poincaré inequalities and Wasserstein contraction using variable curvature bounds ⋮ On Poincaré and Logarithmic Sobolev Inequalities for a Class of Singular Gibbs Measures ⋮ An extremal property of the normal distribution, with a discrete analog ⋮ The Friedland–Hayman inequality and Caffarelli’s contraction theorem ⋮ On Stein's method for multivariate self-decomposable laws ⋮ Quantitative estimates for the Bakry-Ledoux isoperimetric inequality ⋮ Existence of Stein kernels under a spectral gap, and discrepancy bounds

Cites Work

• Log-concavity and strong log-concavity: a review
• The Monge-Ampère equation and its applications
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• An introduction to infinite-dimensional analysis
• Polar factorization and monotone rearrangement of vector‐valued functions
• Boundary regularity of maps with convex potentials
• Monotonicity properties of optimal transportation and the FKG and related inequalities

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