Essential Self-Adjointness for Semi-bounded Magnetic Schrِdinger Operators on Non-compact Manifolds

We prove essential self-adjointness for semi-bounded below magnetic Schrödinger 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.