Flipping Heegaard splittings and minimal surfaces

Autor:	Ketover, Daniel
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematics - Geometric Topology
Druh dokumentu:	Working Paper
Popis:	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. Comment: 55 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.03745 Zobrazit plný text záznamu View this record from Arxiv