Self-adjointness of the Gaffney Laplacian on Vector Bundles
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.
Mathematical Physics Analysis and Geometry
Digital Object Identifier (DOI)
Bandara, & Milatovic, O. (2015). Self-adjointness of the Gaffney Laplacian on Vector Bundles. Mathematical Physics, Analysis, and Geometry, 18(1), 1–. https://doi.org/10.1007/s11040-015-9188-3