Small Curvature Surfaces in Hyperbolic 3-manifolds

@inproceedings{Leininger2005SmallCS,
  title={Small Curvature Surfaces in Hyperbolic 3-manifolds},
  author={Christopher J. Leininger},
  year={2005}
}
In a paper of Menasco and Reid, it is conjectured that there exist no hyperbolic knots in S3 for which the complement contains a closed embedded totally geodesic surface. In this note, we show that one can get ”as close as possible” to a counter-example. Specifically, we construct a sequence of hyperbolic knots {Kn} with complements containing closed embedded essential surfaces having principal curvatures converging to zero as n tends to infinity. We also construct a family of two-component… CONTINUE READING
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Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 29 references

Spherical space forms and Dehn filling

  • S. A. Bleiler, C. D. Hodgson
  • Topology 35
  • 1996
Highly Influential
5 Excerpts

Totally geodesic surfaces in hyperbolic link complements

  • W. Menasco, A. Reid
  • Topology ’90
  • 1990
Highly Influential
4 Excerpts

Thrice-punctured spheres in hyperbolic 3-manifolds

  • C. Adams
  • Trans, Amer. Math. Soc. 287
  • 1985
Highly Influential
4 Excerpts

Problems in low-dimensional topology

  • R. Kirby
  • W. Kazez (Ed.), Geometric Toplogy Proceedings of…
  • 1997
Highly Influential
1 Excerpt

Lectures on Hyperbolic Geometry

  • R. Benedetti, C. Petronio
  • Springer-Verlag Berlin Heidelberg
  • 1992
Highly Influential
3 Excerpts

Gordon

  • C. McA
  • Links and their complements, Topology and…
  • 2002

Complements of hyperbolic knots of braid index four contain no closed embedded totally geodesic surfaces

  • H. Matsuda
  • Topology Appl. 119
  • 2001
1 Excerpt

and J

  • M. Boileau, B. Leeb
  • Porti Uniformization of small 3-orbifolds, C. R…
  • 2001
1 Excerpt

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