Communications in Analysis and Geometry
Volume 29 (2021)
Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds
Pages: 1127 – 1156
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.
S.L. and N.P. acknowledge the financial support of the EPSRC Grant EP/K016687/1 “Topology, Geometry and Laplacians of Simplicial Complexes”.
Received 9 September 2016
Accepted 30 December 2018
Published 1 December 2021