Pitts–Rubinstein conjecture on strongly irreducible Heegaard surfaces
Let a strongly irreducible Heegaard surface lie in a Riemannian three-manifold. Pitts–Rubinstein conjecture. It is either isotopic to a minimal surface of index at most , or isotopic after a single compression to the boundary of a tubular neighborhood of a stable one-sided Heegaard surface. This conjecture was recently resolved and underlies effective finiteness results for irreducible Heegaard splittings.
References
Primary source
Tobias Holck Colding, David Gabai and Daniel Ketover, “Geometric Methods In Heegaard Theory”, arXiv:2002.00445 (2020).
Additional references
2 papers in this index state this conjecture (2019–2020). The statement above is taken from the most recent of them; the others are arXiv:1911.07161.
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