Asymptotic behaviour of the Hodge Laplacian spectrum on graph-like manifolds

  • Michela Egidi

    Durham University, UK
  • Olaf Post

    Durham University, UK

Abstract

We consider a family of compact, oriented and connected -dimensional manifolds shrinking to a metric graph as and describe the asymptotic behaviour of the eigenvalues of its Hodge Laplacian on . We apply our results to produce manifolds with spectral gaps of arbitrarily large size in the spectrum of the Hodge Laplacian.

Cite this article

Michela Egidi, Olaf Post, Asymptotic behaviour of the Hodge Laplacian spectrum on graph-like manifolds. J. Spectr. Theory 7 (2017), no. 2, pp. 433–469

DOI 10.4171/JST/168