论文标题
Frankel的财产和无穷大的最大原则，用于完全最小的超曲面
Frankel property and Maximum Principle at Infinity for complete minimal hypersurfaces
论文作者
论文摘要
在本文中，我们研究了Riemannian $ n- $歧管$ \ MATHCAL {M}^n $的完整最小的Hypersurfaces $ N \ leq N \ leq 7 $，我们以$ n = 3 $的著名工作的精神获得了一些成果。 主要贡献包括将安德森和罗德里格斯的工作扩展到更高的维度。具体而言，我们表明，在具有非负截面曲率和正标曲率的四维流形中，两个不连接的最小层次呈最小的高度凸起，将平板等距与一个高度表面的产物结合到一个间隔。 我们的结果是在无穷大的最大原理基础上，对于两边，抛物线，正确嵌入的最小超曲面的最小超曲面，在有界几何的完整riemannian歧管中，将Mazet在维度中的工作概括为三个尺寸的工作。我们还利用了Chodosh，Li和Stryker最近对完整双面稳定最小曲面的最小稳定最小曲面的分类。
In this paper, we study complete minimal hypersurfaces in Riemannian $n-$manifolds $\mathcal{M}^n$ for dimensions $4 \leq n \leq 7$, and we obtain some results in the spirit of known work for $n=3$. Key contributions include extending the work of Anderson and Rodríguez to higher dimensions. Specifically, we show that in four-dimensional manifolds with nonnegative sectional curvature and positive scalar curvature, two disjoint properly embedded minimal hypersurfaces bound a slab isometric to the product of one hypersurface with an interval. Our results are grounded in a maximum principle at infinity for two-sided, parabolic, properly embedded minimal hypersurfaces in complete Riemannian manifolds of bounded geometry, generalizing the work of Mazet in dimension three to higher dimensions. We also leverage the recent classification of complete two-sided stable minimal hypersurfaces by Chodosh, Li, and Stryker.
