LOWER BOUNDS FOR THE SPECTRAL GAP AND AN EXTENSION OF THE BONNET-MYERS THEOREM
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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 .Read less <
English Keywords
Schrödinger operators
Hodge-de Rham Laplacians
the spectral bound
the spectral gap
Ornstein-Uhlenbeck type operators
perturbations of radial measures. Contents
Origin
Hal imported