Spectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds

dc.creatorCanary, Richard D.
dc.creatorMinsky, Yair N.
dc.creatorTaylor, Edward C.
dc.date1998-10-19
dc.date.accessioned2026-07-07T05:26:33Z
dc.date.available2026-07-07T05:26:33Z
dc.descriptionLet M be a compact 3-manifold whose interior admits a complete hyperbolic structure. We let Lambda(M) be the supremum of the bottom eigenvalue of the Laplacian of N, where N varies over all hyperbolic 3-manifolds homeomorphic to the interior of M. Similarly, we let D(M) be the infimum of the Hausdorff dimensions of limit sets of Kleinian groups whose quotients are homeomorphic to the interior of M. We observe that Lambda(M)=D(M)(2-D(M)) if M is not handlebody or a thickened torus. We characterize exactly when Lambda(M)=1 and D(M)=1 in terms of the characteristic submanifold of the incompressible core of M.
dc.description31 pages; to appear in J. Geom. Anal
dc.identifierhttps://arxiv.org/abs/math/9810124
dc.identifierhttp://arxiv.org/abs/math/9810124
dc.identifierJ. Geom. Analysis 9 (1999), 18-40
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77587
dc.subjectGeometric Topology
dc.titleSpectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds
dc.typetext

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