论文标题
最小值最小的超曲面的改进的Morse指数结合
An Improved Morse Index Bound of Min-Max Minimal Hypersurfaces
论文作者
论文摘要
在本文中，我们在任何封闭的Riemannian歧管$ M^{n+1} $ $（N+1 \ GEQ 3 $）中提供了最小的摩尔斯指数限制的最小超曲面的限制，从而使X.新颖的技术是层次变形的构建和限制性的最低理论。这些技术不依赖颠簸的指标，因此可以适应许多其他Min-Max设置。
In this paper, we give an improved Morse index bound of minimal hypersurfaces from Almgren-Pitts min-max construction in any closed Riemannian manifold $M^{n+1}$ $(n+1 \geq 3$), which generalizes a result by X. Zhou \cite{zhou_multiplicity_2019} for $3 \leq n+1 \leq 7$. The novel techniques are the construction of hierarchical deformations and the restrictive min-max theory. These techniques do not rely on bumpy metrics, and thus could be adapted to many other min-max settings.
