JournalsjstVol. 13, No. 4pp. 1297–1343

Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms

  • Michela Egidi

    Universität Rostock, Germany

  • Katie Gittins

    Durham University, UK

  • Georges Habib

    Lebanese University, Fanar-Matn, Lebanon; Université de Lorraine, Nancy, France

  • Norbert Peyerimhoff

    Durham University, UK
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Abstract

In this paper we introduce the magnetic Hodge Laplacian, which is a generalization of the magnetic Laplacian on functions to differential forms. We consider various spectral results, which are known for the magnetic Laplacian on functions or for the Hodge Laplacian on differential forms, and discuss similarities and differences of this new “magnetic-type” operator.

Cite this article

Michela Egidi, Katie Gittins, Georges Habib, Norbert Peyerimhoff, Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms. J. Spectr. Theory 13 (2023), no. 4, pp. 1297–1343

DOI 10.4171/JST/480