#### Volume 9, issue 2 (2009)

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Small curvature laminations in hyperbolic $3$–manifolds

### William Breslin

Algebraic & Geometric Topology 9 (2009) 723–729
##### Abstract

We show that if $\mathsc{ℒ}$ is a codimension-one lamination in a finite volume hyperbolic $3$–manifold such that the principal curvatures of each leaf of $\mathsc{ℒ}$ are all in the interval $\left(-\delta ,\delta \right)$ for a fixed $\delta$ with $0\le \delta <1$ and no complementary region of $\mathsc{ℒ}$ is an interval bundle over a surface, then each boundary leaf of $\mathsc{ℒ}$ has a nontrivial fundamental group. We also prove existence of a fixed constant ${\delta }_{0}>0$ such that if $\mathsc{ℒ}$ is a codimension-one lamination in a finite volume hyperbolic $3$–manifold such that the principal curvatures of each leaf of $\mathsc{ℒ}$ are all in the interval $\left(-{\delta }_{0},{\delta }_{0}\right)$ and no complementary region of $\mathsc{ℒ}$ is an interval bundle over a surface, then each boundary leaf of $\mathsc{ℒ}$ has a noncyclic fundamental group.

##### Keywords
hyperbolic manifold, lamination
Primary: 57M50