Existence of Bound States for Layers Built Over Hypersurfaces of Euclidean Space

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dc.creatorLin, Christopher
dc.creatorLu, Zhiqin
dc.date2004-02-16
dc.date2007-02-02
dc.date.accessioned2026-07-07T08:18:51Z
dc.date.available2026-07-07T08:18:51Z
dc.descriptionIn this paper, we study the bound states of quantum layers. We prove that for the quantum layer built over a parabolic manifold which is not totally geodesic, if the second fundamantal form decays sufficiently fast, then the bound states exist. In the 2d case, we prove that the quantum layer over a convex surface whose second fundamental form tends to zero at infinity must have bound states.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0402252
dc.identifierhttp://arxiv.org/abs/math/0402252
dc.identifierJ. Funct. Anal., 244(1): 1-25, 2007.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134576
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject58C40; 58E35
dc.titleExistence of Bound States for Layers Built Over Hypersurfaces of Euclidean Space
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