Approximations of the connection Laplacian spectra

Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev, Jinpeng Lu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider a convolution-type operator on vector bundles over metric-measure spaces. This operator extends the analogous convolution Laplacian on functions in our earlier work to vector bundles, and is a natural extension of the graph connection Laplacian. We prove that for Euclidean or Hermitian connections on closed Riemannian manifolds, the spectrum of this operator and that of the graph connection Laplacian both approximate the spectrum of the connection Laplacian.

Original languageEnglish (US)
Pages (from-to)3185-3206
Number of pages22
JournalMathematische Zeitschrift
Issue number3
StatePublished - Jul 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics


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