Communications in Analysis and Geometry

Volume 29 (2021)

Number 5

Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds

Pages: 1127 – 1156



Michela Egidi (Fakultät für Mathematik, Ruhr-Universität Bochum, Germany; and Institut für Mathematik, Rostock Universität, Rostock, Germany)

Shiping Liu (School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui Province, China)

Florentin Münch (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)

Norbert Peyerimhoff (Department of Mathematical Sciences, Durham University, Durham, United Kingdom)


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.

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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