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Eigenfunctions of the Laplacian and boundary behaviour on manifolds of hyperbolic type

Published online by Cambridge University Press:  01 November 1997

N. MANDOUVALOS  and
M. MARIAS
N. MANDOUVALOS
Affiliation:
Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54006, Greece; e-mail: marias@olympccf.auth.gr
M. MARIAS
Affiliation:
Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54006, Greece; e-mail: marias@olympccf.auth.gr
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Abstract

We describe a method of constructing explicitly eigenfunctions of the Laplacian with a prescribed boundary behaviour on a class of manifolds of hyperbolic type. These are manifolds of the form M=X×R×+, where X is an n-dimensional Riemannian manifold and the metric of M is a perturbation of the hyperbolic one.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 3 , November 1997 , pp. 551 - 564
Copyright
Cambridge Philosophical Society 1997

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