论文标题
最小的最小超级表面具有较高的多重性
Min-max minimal hypersurfaces with higher multiplicity
论文作者
论文摘要
我们展示了$（n+1）$ - sphere（$ 2 \ leq n \ leq 6 $）上的非笨拙指标的第一个示例，其中与两参数min-max构造相关的varifold必须是一个多重性二$ n $ n $ sphere。这是由摩尔斯索引两种最小的超曲面的新区域和分离估算所证明的。我们还构建了非颠簸的投射空间，其中第一个最小的最大超曲面是单方面的，而自由边界最小值最大超曲面则不当。
We exhibit the first set of examples of non-bumpy metrics on the $(n+1)$-sphere ($2\leq n\leq 6$) in which the varifold associated with the two-parameter min-max construction must be a multiplicity-two minimal $n$-sphere. This is proved by a new area-and-separation estimate for certain minimal hypersurfaces with Morse index two inspired by an early work of Colding-Minicozzi. We also construct non-bumpy projective spaces in which the first min-max hypersurfaces are one-sided, and non-bumpy balls in which the free boundary min-max hypersurfaces are improper.
