Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem

Fuente: arXiv
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Main Authors: Bonnefont, Michel, Ouhabaz, El Maati
Format: Preprint
Published: 2021
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author Bonnefont, Michel
Ouhabaz, El Maati
author_facet Bonnefont, Michel
Ouhabaz, El Maati
contents On a fairly general class of Riemannian manifolds M, we prove lower estimates in terms of the Ricci curvature for the spectral bound (when M has infinite volume) and for the spectral gap (when M has finite volume) for the Laplace-Beltrami operator. As a byproduct of our results we obtain an extension of the Bonnet-Myers theorem on the compactness of the manifold. We also prove lower bounds for the spectral gap for Ornstein-Uhlenbeck type operators on weighted manifolds. As an application we prove lower bounds for the spectral gap of perturbations of some radial measures on R n .
format Preprint
id arxiv_https___arxiv_org_abs_2112_03542
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem
Bonnefont, Michel
Ouhabaz, El Maati
Analysis of PDEs
Functional Analysis
Spectral Theory
On a fairly general class of Riemannian manifolds M, we prove lower estimates in terms of the Ricci curvature for the spectral bound (when M has infinite volume) and for the spectral gap (when M has finite volume) for the Laplace-Beltrami operator. As a byproduct of our results we obtain an extension of the Bonnet-Myers theorem on the compactness of the manifold. We also prove lower bounds for the spectral gap for Ornstein-Uhlenbeck type operators on weighted manifolds. As an application we prove lower bounds for the spectral gap of perturbations of some radial measures on R n .
title Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem
topic Analysis of PDEs
Functional Analysis
Spectral Theory
url https://arxiv.org/abs/2112.03542