Abstract:The main subject of this thesis are a certain class of hyperbolic 3-manifolds called quasi-Fuchsian manifold. Given an orientied, closed hyperbolic surface S, these manifolds are homeomorphic to S × R. We study two questions regarding them: one is on measured foliations at infinity and the other is on foliation by constant mean curvature surfaces.Measured foliations at infinity of quasi-Fuchsian manifolds are a natural analog at infinity to the measured bending laminations on the boundary of its convex core. G… Show more
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