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Publikation: Working paper/Preprint › Working paper › Forskning

**Absence of embedded eigenvalues for Riemannian Laplacians.** / Ito, Kenichi; Skibsted, Erik.

Publikation: Working paper/Preprint › Working paper › Forskning

Ito, K & Skibsted, E 2011 'Absence of embedded eigenvalues for Riemannian Laplacians' Preprints, nr. 4, Department of Mathematics, Aarhus University.

Ito, K., & Skibsted, E. (2011). *Absence of embedded eigenvalues for Riemannian Laplacians*. Department of Mathematics, Aarhus University. Preprints Nr. 4

Ito K, Skibsted E. 2011. Absence of embedded eigenvalues for Riemannian Laplacians. Department of Mathematics, Aarhus University.

Ito, Kenichi og Erik Skibsted *Absence of embedded eigenvalues for Riemannian Laplacians*. Department of Mathematics, Aarhus University. (Preprints; Journal nr. 4). 2011., 16 s.

Ito K, Skibsted E. Absence of embedded eigenvalues for Riemannian Laplacians. Department of Mathematics, Aarhus University. 2011 sep. 9.

Ito, Kenichi ; Skibsted, Erik. / **Absence of embedded eigenvalues for Riemannian Laplacians**. Department of Mathematics, Aarhus University, 2011. (Preprints; Nr. 4).

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title = "Absence of embedded eigenvalues for Riemannian Laplacians",

abstract = "Schr{\"o}dinger 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{\"o}dinger operator and the unique continuation property. Examples include ends endowed with asymptotic Euclidean or hyperbolic metrics studied previously in the literature.",

author = "Kenichi Ito and Erik Skibsted",

year = "2011",

month = sep,

day = "9",

language = "English",

series = "Preprints",

publisher = "Department of Mathematics, Aarhus University",

number = "4",

type = "WorkingPaper",

institution = "Department of Mathematics, Aarhus University",

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T1 - Absence of embedded eigenvalues for Riemannian Laplacians

AU - Ito, Kenichi

AU - Skibsted, Erik

PY - 2011/9/9

Y1 - 2011/9/9

N2 - 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.

AB - 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.

M3 - Working paper

T3 - Preprints

BT - Absence of embedded eigenvalues for Riemannian Laplacians

PB - Department of Mathematics, Aarhus University

ER -