Polyhedral metrics on the boundaries of convex compact quasi-Fuchsian manifolds
نویسندگان
چکیده
منابع مشابه
Quasi-fuchsian 3-manifolds and Metrics on Teichm¨uller Space
An almost Fuchsian 3-manifold is a quasi-Fuchsian manifold which contains an incompressible closed minimal surface with principal curvatures in the range of (−1, 1). Such a 3-manifold M admits a foliation of parallel surfaces, whose locus in Teichmüller space is represented as a path γ, we show that γ joins the conformal structures of the two components of the conformal boundary of M . Moreover...
متن کاملQuasi-fuchsian Manifolds with Particles
We consider 3-dimensional hyperbolic cone-manifolds which are “convex cocompact” in a natural sense, with cone singularities along infinite lines. Such singularities are sometimes used by physicists as models for massive spinless point particles. We prove an infinitesimal rigidity statement when the angles around the singular lines are less than π: any infinitesimal deformation changes either t...
متن کاملNoncompact Fuchsian and quasi-Fuchsian surfacesin hyperbolic 3--manifolds
Given a noncompact quasi-Fuchsian surface in a finite volume hyperbolic 3–manifold, we introduce a new invariant called the cusp thickness, that measures how far the surface is from being totally geodesic. We relate this new invariant to the width of a surface, which allows us to extend and generalize results known for totally geodesic surfaces. We also show that checkerboard surfaces provide e...
متن کاملFoliations for Quasi-fuchsian 3-manifolds
In this paper, we prove that if a quasi-Fuchsian 3-manifold contains a minimal surface whose principle curvature is less than 1, then it admits a foliation such that each leaf is a surface of constant mean curvature. The key method that we use here is volume preserving mean curvature flow.
متن کاملGeometric Evolution Equations and Foliations on Quasi-fuchsian Three-manifolds
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 t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2014
ISSN: 1631-073X
DOI: 10.1016/j.crma.2014.09.001