590 research outputs found
Geometric inflexibility and 3-manifolds that fiber over the circle
We prove hyperbolic 3-manifolds are geometrically inflexible: a unit
quasiconformal deformation of a Kleinian group extends to an equivariant
bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz
constant decays exponentially in the distance form the boundary of the convex
core for points in the thick part. Estimates at points in the thin part are
controlled by similar estimates on the complex lengths of short curves. We use
this inflexibility to give a new proof of the convergence of pseudo-Anosov
double-iteration on the quasi-Fuchsian space of a closed surface, and the
resulting hyperbolization theorem for closed 3-manifolds that fiber over the
circle with pseudo-Anosov monodromy.Comment: 52 pages. Final version. Appeared in Journal of Topology. Material in
original version on inflexibility of hyperbolic cone-manifolds has been
rewritten into a new paper with identifier arXiv:1412.463
Cone-manifolds and the density conjecture
We give an expository account of our proof that each cusp-free hyperbolic
3-manifold M with finitely generated fundamental group and incompressible ends
is an algebraic limit of geometrically finite hyperbolic 3-manifolds.Comment: 19 Pages, 2 figures; to appear, proceedings of the Warwick
Conference: Kleinian Groups and Hyperbolic 3-Manfiolds, September 200
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