Principal curvatures of fibers and Heegaard surfaces

Details Principal curvatures of fibers and Heegaard surfaces Principal curvatures of fibers and Heegaard surfaces

2010-02-04

arxiv.org/abs/1002.1065v1

Mathematics

Geometric Topology

6 pages

Scientific paper

We study principal curvatures of fibers and Heegaard surfaces smoothly embedded in hyperbolic 3-manifolds. It is well known that a fiber or a Heegaard surface in a hyperbolic 3-manifold cannot have principal curvatures everywhere less than one in absolute value. We show that given an upper bound on the genus of a minimally embedded fiber or Heegaard surface and a lower bound on the injectivity radius of the hyperbolic 3-manifold, there exists a $\delta > 0$ such that the fiber or Heegaard surface must contain a point at which one of the principal curvatures is greater than $1 + \delta$ in absolute value.

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