The Laplace operator on hyperbolic three manifolds with cusps of non- maximal rank
The generalized eigenfunction expansion for the Laplace operator on a hyperbolic 3-manifold \(M=\mathbb{H}/\Gamma\) is studied, where \(\Gamma\) is a geometrically finite discrete group of orientation preserving isometries, which may contain parabolic elements of non-maximal rank. The existence of a continuum eigenfunction expansion is proved and it is shown that in the spectral parameter the eigenfunctions (Eisenstein series for \(\Gamma)\) have meromorphic continuations to \(\mathbb{C}\backslash\{1\}\).
scientific article; zbMATH DE number 59804
scientific article