Essential self-adjointness for semi-bounded magnetic Schrodinger operators on non-compact manifolds

We prove essential self-adjointness for semi-bounded below magnetic Schrodinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar potential are allowed. This is an extension of the Povzner-Wienholtz-Simader theorem. The proof uses the scheme of Wienholtz but requires a refined invariant integration by parts, technique, as well as the use of a family of cut-off functions which are constructed by a non-trivial smoothing procedure due to Karcher. (C) 2001 Academic Press.