Principal curvatures of fibers and Heegaard surfaces

2010/02/04 by William Breslin, Breslin, William
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1002.1065

6 pages

arxiv created 2010/02/04 · arxiv updated 2010/02/26

Abstract

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 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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