Spectral stability of metric-measure Laplacians

Dmitri Burago; Sergei Ivanov; Yaroslav Kurylev

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arXiv · 1506.06781

Spectral stability of metric-measure Laplacians

Dmitri Burago·Sergei Ivanov·Yaroslav Kurylev

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Abstract

We consider a "convolution mm-Laplacian" operator on metric-measure spaces and study its spectral properties. The definition is based on averaging over small metric balls. For reasonably nice metric-measure spaces we prove stability of convolution Laplacian's spectrum with respect to metric-measure perturbations and obtain Weyl-type estimates on the number of eigenvalues.

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Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev. 2015-06-22. Spectral stability of metric-measure Laplacians. https://arxiv.org/abs/1506.06781

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