From the Boundary of the Convex Core to the Conformal Boundary |
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| Authors: | Martin Bridgeman Richard D Canary |
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| Institution: | (1) Department of Mathematics, Boston College, Chestnut Hill, MA, 02167, U.S.A.;(2) Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, U.S.A. |
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| Abstract: | If N is a hyperbolic 3-manifold with finitely generated fundamental group, then the nearest point retraction is a proper homotopy equivalence from the conformal boundary of N to the boundary of the convex core of N. We show that the nearest point retraction is Lipschitz and has a Lipschitz homotopy inverse and that one may bound the Lipschitz constants in terms of the length of the shortest compressible curve on the conformal boundary. |
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| Keywords: | Kleinian group hyperbolic manifold convex core limit set |
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