Geodesic
Curvature Bounds for Surfaces in Hyperbolic 3-Manifolds
Canadian journal of mathematics, Tome 62 (2010) no. 5, pp. 994-1010

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DOI

A triangulation of a hyperbolic 3-manifold is $L$ -thick if each tetrahedron having all vertices in the thick part of $M$ is $L$ -bilipschitz diffeomorphic to the standard Euclidean tetrahedron. We show that there exists a fixed constant $L$ such that every complete hyperbolic 3-manifold has an $L$ -thick geodesic triangulation. We use this to prove the existence of universal bounds on the principal curvatures of ${{\pi }_{1}}$ -injective surfaces and strongly irreducible Heegaard surfaces in hyperbolic 3-manifolds.
DOI : 10.4153/CJM-2010-056-8
Mots-clés : 57M50 
Breslin, William. Curvature Bounds for Surfaces in Hyperbolic 3-Manifolds. Canadian journal of mathematics, Tome 62 (2010) no. 5, pp. 994-1010. doi: 10.4153/CJM-2010-056-8
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     title = {Curvature {Bounds} for {Surfaces} in {Hyperbolic} {3-Manifolds}},
     journal = {Canadian journal of mathematics},
     pages = {994--1010},
     year = {2010},
     volume = {62},
     number = {5},
     doi = {10.4153/CJM-2010-056-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-056-8/}
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