Principal Curvatures of Fibers and Heegaard Surfaces
نویسنده
چکیده
We study principal curvatures of fibers and Heeagaard 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 δ > 0 such that the fiber or Heegaard surface must contain a point at which one of the principal curvatures is greater than 1+ δ in absolute value.
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