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arXiv · 2211.03745

Flipping Heegaard splittings and minimal surfaces

Daniel Ketover
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Abstract

We show that the number of genus $g$ embedded minimal surfaces in $\mathbb{S}^3$ tends to infinity as $g\rightarrow\infty$. The surfaces we construct resemble doublings of the Clifford torus with curvature blowing up along torus knots as $g\rightarrow\infty$, and arise from a two-parameter min-max scheme in lens spaces. More generally, by stabilizing and flipping Heegaard foliations we produce index at most $2$ minimal surfaces with controlled topological type in arbitrary Riemannian three-manifolds.

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Daniel Ketover. 2022-11-07. Flipping Heegaard splittings and minimal surfaces. https://arxiv.org/abs/2211.03745

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