Schrödinger operators on non-compact connected Riemannian manifolds. A principal example is given by a manifold with an end (possibly more than one) in which geodesic coordinates are naturally defined. In this case one of our geometric conditions is a positive lower bound of the second fundamental form of angular submanifolds at infinity inside the end. Another condition may be viewed (at least in a special case) as being a bound of the trace of this quantity, while similarly, a third one as being a bound of the derivative of this trace. In addition to geometric bounds we need conditions on the potential, a regularity property of the domain of the Schrödinger operator and the unique continuation property. Examples include ends endowed with asymptotic Euclidean or hyperbolic metrics studied previously in the literature.

Originalsprog | Engelsk |
---|

Udgiver | Department of Mathematics, Aarhus University |
---|

Antal sider | 16 |
---|

Status | Udgivet - 9 sep. 2011 |
---|

Navn | Preprints |
---|

Nummer | 4 |
---|

ISSN | 1397-4076 |
---|