论文标题
翻转Heegaard分裂和最小表面
Flipping Heegaard splittings and minimal surfaces
论文作者
论文摘要
我们表明，$ g $ g $嵌入式最小表面的数量在$ \ mathbb {s}^3 $中趋向于无穷大，以$ g \ rightarrow \ infty \ infty $。我们构建的表面类似于克利福德圆环的双倍，曲率沿着圆环结的曲率为$ g \ rightarrow \ infty $，并且来自镜头空间中的两参数min-max方案。更普遍的是，通过稳定和翻转Heegaard叶子，我们生成的指数最多$ 2 $最小的表面，并在任意的Riemannian三元中使用受控拓扑类型。
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.
