Absence of embedded eigenvalues for Riemannian Laplacians

Kenichi Ito, Erik Skibsted

Publikation: Working paper/Preprint Working paperForskning

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Abstract

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.
OriginalsprogEngelsk
UdgiverDepartment of Mathematics, Aarhus University
Antal sider16
StatusUdgivet - 9 sep. 2011
NavnPreprints
Nummer4
ISSN1397-4076

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