Approximations of the connection Laplacian spectra
Analysis of PDEs
2022-02-23 v2 Differential Geometry
Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2012.09997,
title = {Approximations of the connection Laplacian spectra},
author = {Dmitri Burago and Sergei Ivanov and Yaroslav Kurylev and Jinpeng Lu},
journal= {arXiv preprint arXiv:2012.09997},
year = {2022}
}
Comments
journal version, revised Lemma 4.1, added references