Self-adjointness of the Gaffney Laplacian on vector bundles
Functional Analysis
2016-03-09 v2 Differential Geometry
Spectral Theory
Abstract
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.
Keywords
Cite
@article{arxiv.1409.5212,
title = {Self-adjointness of the Gaffney Laplacian on vector bundles},
author = {Lashi Bandara and Ognjen Milatovic},
journal= {arXiv preprint arXiv:1409.5212},
year = {2016}
}
Comments
Sharpened/strengthened Lemma 3.1, fixed typos, added some additional and relevant definitions to the preliminaries