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Curvature Bounds for Surfaces in Hyperbolic 3-Manifolds

Published online by Cambridge University Press:  20 November 2018

William Breslin
William Breslin*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI, U.S.A.
*
[email protected]
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Abstract

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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.

Keywords

57M50
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 5 , 01 October 2010 , pp. 994 - 1010
Copyright
Copyright © Canadian Mathematical Society 2010

Footnotes

This work was partially supported by the NSF grant DMS-0135345.

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