Self-adjointness of the Gaffney Laplacian on Vector Bundles
Journal article, 2015

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.

Essential self-adjointness

Gaffney Laplacian

Geodesically incomplete manifold

Polar boundary

Sobolev space

Negligible boundary

Bochner Laplacian

Author

Menaka Lashitha Bandara

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

O. Milatovic

University of North Florida

Mathematical Physics Analysis and Geometry

1385-0172 (ISSN) 1572-9656 (eISSN)

Vol. 18 1 artikel nr 17-

Subject Categories

Geometry

DOI

10.1007/s11040-015-9188-3

More information

Created

10/8/2017