A graph discretization of the Laplace–Beltrami operator

Dmitri Burago; Sergei Ivanov; Yaroslav Kurylev

doi:10.4171/jst/83

JournalsjstVol. 4, No. 4pp. 675–714

A graph discretization of the Laplace–Beltrami operator

Dmitri Burago
The Pennsylvania State University, University Park, USA
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Sergei Ivanov
Russian Academy of Sciences, St. Petersburg, Russian Federation
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Yaroslav Kurylev
University College London, UK
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- zbMATH Open

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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