Determinants of Laplacians and Isopolar Metrics on Surfaces of Infinite Area

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dc.creatorBorthwick, D.
dc.creatorJudge, C.
dc.creatorPerry, P. A.
dc.date2001-11-19
dc.date.accessioned2026-07-07T04:44:41Z
dc.date.available2026-07-07T04:44:41Z
dc.descriptionWe construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalues and resonances of the Laplacian. In the hyperbolic near infinity case the determinant is analyzed through the zeta-regularized relative determinant for a conformal metric perturbation. We establish that this relative determinant is a ratio of entire functions of order two with divisor corresponding to eigenvalues and resonances of the perturbed and unperturbed metrics. These results are applied to the problem of compactness in the smooth topology for the class of metrics with a given set of eigenvalues and resonances.
dc.description33 pages, AMS-LaTeX
dc.identifierhttps://arxiv.org/abs/math/0111211
dc.identifierhttp://arxiv.org/abs/math/0111211
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62686
dc.subjectDifferential Geometry
dc.subjectSpectral Theory
dc.subject58J50,35P25
dc.titleDeterminants of Laplacians and Isopolar Metrics on Surfaces of Infinite Area
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