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**ABSTRACT:**Given a complete noncompact surface Sigma embedded in R3, we consider the Dirichlet Laplacian in the layer Omega that is defined as a tubular neighborhood of constant width about Sigma. Using an intrinsic approach to the geometry of Omega, we generalize the spectral results of the original paper by Duclos et al. [Commun. Math. Phys. 223, 13 (2001)] to the situation when Sigma does not possess poles. This enables us to consider topologically more complicated layers and state new spectral results. In particular, we are interested in layers built over surfaces with handles or several cylindrically symmetric ends. We also discuss more general regions obtained by compact deformations of certain Omega.Journal of Mathematical Physics 02/2004; 45(2). · 1.18 Impact Factor - 01/1964;
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**ABSTRACT:**[Habschr. ETH Zürich] 1957.Commentarii Mathematici Helvetici 01/1958; · 0.90 Impact Factor

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