English

Spectral stability of metric-measure Laplacians

Spectral Theory 2018-08-28 v4 Metric Geometry

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.

Keywords

Cite

@article{arxiv.1506.06781,
  title  = {Spectral stability of metric-measure Laplacians},
  author = {Dmitri Burago and Sergei Ivanov and Yaroslav Kurylev},
  journal= {arXiv preprint arXiv:1506.06781},
  year   = {2018}
}

Comments

v4: more references and clarifications suggested by the referees