Absence of embedded eigenvalues for Riemannian Laplacians

Details Absence of embedded eigenvalues for Riemannian Laplacians Absence of embedded eigenvalues for Riemannian Laplacians

2011-09-09

arxiv.org/abs/1109.1928v1

Physics

Mathematical Physics

Scientific paper

In this paper we study absence of embedded eigenvalues for Schr\"odinger 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 Schr\"odinger operator and the unique continuation property. Examples include ends endowed with asymptotic Euclidean or hyperbolic metrics studied previously in the literature.

Affiliated with

Also associated with

No associations

Rating

Absence of embedded eigenvalues for Riemannian Laplacians does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Absence of embedded eigenvalues for Riemannian Laplacians, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Absence of embedded eigenvalues for Riemannian Laplacians will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-413192