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arXiv 2012.099972020-12math.APmath.DGmath.SP

Approximations of the connection Laplacian spectra

Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev, Jinpeng Lu

备注：: journal version, revised Lemma 4.1, added references

英文摘要：

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.

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