Self-adjointness of the Gaffney Laplacian on vector bundles

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.

Sharpened/strengthened Lemma 3.1, fixed typos, added some additional and relevant definitions to the preliminaries

References in corpus (2)

• Density problems on vector bundles and manifolds
• The Kato square root problem on vector bundles with generalised bounded geometry