Small Curvature Surfaces in Hyperbolic 3-manifolds

  title={Small Curvature Surfaces in Hyperbolic 3-manifolds},
  author={Christopher J. Leininger},
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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