JournalsjstVol. 4, No. 4pp. 675–714

A graph discretization of the Laplace–Beltrami operator

  • Dmitri Burago

    The Pennsylvania State University, University Park, USA

  • Sergei Ivanov

    Russian Academy of Sciences, St. Petersburg, Russian Federation

  • Yaroslav Kurylev

    University College London, UK
A graph discretization of the Laplace–Beltrami operator cover
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Abstract

We show that eigenvalues and eigenfunctions of the Laplace–Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.

Cite this article

Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev, A graph discretization of the Laplace–Beltrami operator. J. Spectr. Theory 4 (2014), no. 4, pp. 675–714

DOI 10.4171/JST/83