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