Low frequency resolvent estimates for long range perturbations of the Euclidean Laplacian

TL;DR

This paper uses Mourre theory to establish sharp low frequency resolvent estimates for long-range perturbations of the Euclidean Laplacian, advancing understanding of spectral properties in perturbed geometries.

Contribution

It introduces a novel application of Mourre theory to obtain sharp low frequency resolvent estimates for long-range metric perturbations.

Findings

Sharp low frequency resolvent estimates achieved

Effective weights for long-range perturbations derived

Enhanced spectral analysis techniques developed

Abstract

Using Mourre theory, we obtain low frequency resolvent estimates with sharp weights for long range metric perturbations of the flat Laplacian.