Absence of embedded eigenvalues for Riemannian Laplacians

作者：Ito K^*; Skibsted E

来源：Advances in Mathematics, 2013, 248: 945-962.

DOI：10.1016/j.aim.2013.08.023

• Spectral theory
• Schrodinger operator
• Riemannian geometry

In this paper we study absence of embedded eigenvalues for Schrodinger 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 is an upper bound of the trace of this quantity, while a third one is a bound of the derivatives of part of the trace (some oscillatory behaviour of the trace is allowed). In addition to geometric bounds we need conditions on the potential, a regularity property of the domain of the Schrodinger operator and the unique continuation property. Examples include ends endowed with asymptotic Euclidean or hyperbolic metrics.

• 出版日期2013-11-25