Geodesic
Small curvature laminations in hyperbolic 3–manifolds
Breslin, William1
1 Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor 48109-1043, United States
Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 723-729

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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 with 0 ≤ δ < 1 and no complementary 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 complementary region of ℒ is an interval bundle over a surface, then each boundary leaf of ℒ has a noncyclic fundamental group.

DOI : 10.2140/agt.2009.9.723
Keywords: hyperbolic manifold, lamination

Breslin, William 1

1 Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor 48109-1043, United States 
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Breslin, William. Small curvature laminations in hyperbolic 3–manifolds. Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 723-729. doi: 10.2140/agt.2009.9.723

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