Stability estimates for the sharp spectral gap bound under a curvature-dimension condition
type: Item
instance of: scholarly article
title: Stability estimates for the sharp spectral gap bound under a curvature-dimension condition
author: Max Fathi
author: Ivan Gentil
author: Jordan Serres
publication date: 2024-10-18T00:00:00Z
review text: The authors study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. \N\NThe main result is a sharp quantitative estimate showing that if the spectral gap of an \(RCD(N - 1, N)\) space is almost minimal, then the pushforward of the measure by an eigenfunction associated with the spectral gap is close to a Beta distribution. The proof combines estimates on the eigenfunction obtained via a new \(L^1\)-functional inequality for RCD spaces with Stein's method for distribution approximation.\N\NThe authors also derive analogous, almost sharp, estimates for infinite and negative values of the dimension parameter.
reviewed by: Pavel Stoynov
Mathematics Subject Classification ID: 60B05
Mathematics Subject Classification ID: 46E27
zbMATH DE Number: 7929010
zbMATH Keywords: spectral gap
zbMATH Keywords: Poincaré inequalities
zbMATH Keywords: RCD spaces
zbMATH Keywords: curvature-dimension condition
zbMATH Keywords: Stein method
MaRDI profile type: Publication
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published in: Annales de l’institut Fourier
DOI: 10.5802/AIF.3608
description: scientific article; zbMATH DE number 7929010