Bernard Maskit Memorial Tribute
This is an expanded version of the Maskit memorial tribute that appeared in the August 2025 issue of the Notices of the AMS.
math.HO↗
arXiv subjects
Edward C. Taylor
Publications and source records attributed to Edward C. Taylor.
Spectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds
Let 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.
math.GT↗