Small Curvature Laminations in Hyperbolic 3-manifolds
نویسنده
چکیده
We show that if L is a codimension-one lamination in a finite volume hyperbolic 3-manifold such that the principal curvatures of each leaf of L are all in the interval (−δ, δ) for a fixed δ ∈ [0, 1) and no complimentary region of L is an interval bundle over a surface, then each boundary leaf of L has a nontrivial fundamental group. We also prove existence of a fixed constant δ0 > 0 such that if L is a codimension-one lamination in a finite volume hyperbolic 3-manifold such that the principal curvatures of each leaf of L are all in the interval (−δ0, δ0) and no complimentary region of L is an interval bundle over a surface, then each boundary leaf of L has a noncyclic fundamental group.
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