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Register a new userOn the construction of minimal foliations by hyperbolic surfaces on 3-manifolds
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We describe several methods to construct minimal foliations by hyperbolic surfaces on closed 3-manifolds, and discuss the properties of the examples thus obtained.
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By work of Uhlenbeck, the largest principal curvature of any least area fiber of a hyperbolic $3$-manifold fibering over the circle is bounded below by one. We give a short argument to show that, along certain families of fibered hyperbolic $3$-manifolds, there is a uniform lower bound for the maximum principal curvatures of a least area minimal surface which is greater than one.
We show that the horocycle flow associated with a foliation on a compact manifold by hyperbolic surfaces is minimal under certain conditions.
The paper contains a new proof that a complete, non-compact hyperbolic $3$-manifold $M$ with finite volume contains an immersed, closed, quasi-Fuchsian surface.
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