Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds

TL;DR

This paper establishes new eigenvalue estimates for the magnetic Laplacian on closed Riemannian manifolds, linking magnetic fields, Ricci curvature, and geometric constants, extending classical spectral geometry results.

Contribution

It introduces Lichnerowicz and Buser type estimates for the magnetic Laplacian, incorporating magnetic potentials into eigenvalue bounds on manifolds.

Findings

Derived lower bounds for eigenvalues using Ricci curvature and magnetic potential.

Established relations between eigenvalues, magnetic fields, and Cheeger constants.

Extended classical estimates to the magnetic Laplacian setting.

Abstract

In this paper, we present a Lichnerowicz type estimate and (higher order) Buser type estimates for the magnetic Laplacian on a closed Riemannian manifold with a magnetic potential. These results relate eigenvalues, magnetic fields, Ricci curvature, and Cheeger type constants.