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- 17Subject Categories
Geometry
DOI
10.1007/s11040-015-9188-3