On the existence of unstable minimal Heegaard surfaces

Daniel Ketover; Yevgeny Liokumovich

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arXiv · 1709.09744

On the existence of unstable minimal Heegaard surfaces

Daniel Ketover·Yevgeny Liokumovich

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Abstract

We prove that for generic metrics on a 3-sphere, the minimal surface obtained from the min-max procedure of Simon-Smith has index 1. We prove an analogous result for minimal surfaces arising from strongly irreducible Heegaard sweepouts in 3-manifolds. We also confirm a conjecture of Pitts-Rubinstein that a strongly irreducible Heegaard splitting in a hyperbolic three-manifold can either be isotoped to a minimal surface of index at most 1 or else after a neck-pinch is isotopic to a one-sided minimal Heegaard surface.

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Daniel Ketover, Yevgeny Liokumovich. 2017-09-27. On the existence of unstable minimal Heegaard surfaces. https://arxiv.org/abs/1709.09744

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