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# Small Curvature Surfaces in Hyperbolic 3-manifolds

@inproceedings{Leininger2005SmallCS, title={Small Curvature Surfaces in Hyperbolic 3-manifolds}, author={Christopher J. Leininger}, year={2005} }

- Published 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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