Stability of Klartag's improved Lichnerowicz inequality

2024/04/18 by Thomas A. Courtade, Courtade, Thomas A., Max Fathi +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Inequalities and Applications #Metric Geometry (math.MG) #Nonlinear Differential Equations Analysis #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2404.12277

openalex publication_date 2024/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent work, Klartag gave an improved version of Lichnerowicz' spectral gap bound for uniformly log-concave measures, which improves on the classical estimate by taking into account the covariance matrix. We analyze the equality cases in Klartag's bound, showing that it can be further improved whenever the measure has no Gaussian factor. Additionally, we give a quantitative improvement for log-concave measures with finite Fisher information.

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