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Geometric evolution equations and foliations on quasi-fuchsian three-manifolds, preprint

By Zheng Huang and Biao Wang


Abstract. For any quasi-Fuchsian 3-manifold M which contains an incompressible closed surface with principal curvatures in the range of (−1, 1), we use method of geometric evolution equations to prove that it admits a unique foliation of constant mean curvature surfaces on M. Applications include uniqueness of prescribed constant mean curvature surfaces, and an upper bound for the hyperbolic volume of the convex core of M. 1

Year: 2009
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