On the existence of unstable minimal Heegaard surfaces
Differential Geometry
2019-11-21 v2 Geometric Topology
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.
Keywords
Cite
@article{arxiv.1709.09744,
title = {On the existence of unstable minimal Heegaard surfaces},
author = {Daniel Ketover and Yevgeny Liokumovich},
journal= {arXiv preprint arXiv:1709.09744},
year = {2019}
}
Comments
This preprint is superseded by arXiv:1911.07161 [math.DG]