Flipping Heegaard splittings and minimal surfaces

2022/11/07 by Ketover, Daniel · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2211.03745

Abstract

We show that the number of genus g embedded minimal surfaces in \mathbbS³ tends to infinity as g→∞. The surfaces we construct resemble doublings of the Clifford torus with curvature blowing up along torus knots as g→∞, 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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• Regularity of Cohomogeneity two equivariant isotopy minimization problems and minimal hypersurfaces with large first Betti number on spheres

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