Curvature Bounds for Surfaces in Hyperbolic 3-Manifolds

Breslin, William

Canadian journal of mathematics, Tome 62 (2010) no. 5, pp. 994-1010

Résumé

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.

Détail

DOI : 10.4153/CJM-2010-056-8

Mots-clés : 57M50

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