On the existence of minimal Heegaard surfaces

2019/11/17 by Daniel Ketover, Ketover, Daniel, Yevgeny Liokumovich +3 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · doi:10.48550/arxiv.1911.07161

Abstract

Let H be a strongly irreducible Heegaard surface in a closed oriented Riemannian 3-manifold. We prove that H is either isotopic to a minimal surface of index at most one or isotopic to the boundary of a tubular neighborhood about a non-orientable minimal surface with a vertical handle attached. This confirms a long-standing conjecture of J. Pitts and J.H. Rubinstein.

Citations

• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature
• A dichotomy for minimal hypersurfaces in manifolds thick at infinity

Cited by

• Mean curvature flow in homology and foliations of hyperbolic\n 3-manifolds

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