The Laplacian on hyperbolic 3-manifolds with Dehn surgery type singularities (Q1049682)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Laplacian on hyperbolic 3-manifolds with Dehn surgery type singularities |
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The Laplacian on hyperbolic 3-manifolds with Dehn surgery type singularities (English)
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13 January 2010
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Let \(\Delta\) be the scalar Laplacian on a complete non-compact hyperbolic \(3\)-manifold \(M\) of finite volume. There are a finite number of eigenvalues \(0=\lambda_0<\lambda_1\leq\dots\leq\lambda_k<1\) below the essential spectrum \([1,\infty)\). The authors study the basic spectral properties in the setting of manifolds with Dehn surgery type singularities and the dependence on the generalized Dehn surgery coefficients.
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hyperbolic Dehn surgery
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eigenvalues of the Laplacian
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Margulis Lemma
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Friedrichs extension
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convergence of small eigenvalues
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Neumann eigenvalues
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Dirichlet eigenvalues
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