论文标题
尺寸8中最小超曲面的通用规律性
Generic Regularity of Minimal Hypersurfaces in Dimension 8
论文作者
论文摘要
在本文中，我们表明，每$ 8 $维的封闭式Riemmanian歧管，带有$ C^\ Infty $ - 类指标，可以承认光滑的最小超出表面。这是N. Smale和Chodosh-Liokumovich-Spolaor的概括性结果。我们的构造与他们的局部扰动技术不同，是基于全球扰动论点和一种新颖的几何不变式的，该几何不变型以合适的权重计数奇异点。
In this paper, we show that every $8$-dimensional closed Riemmanian manifold with $C^\infty$-generic metrics admits a smooth minimal hypersurface. This generalized previous results by N. Smale and Chodosh-Liokumovich-Spolaor. Different from their local perturbation techniques, our construction is based on a global perturbation argument in and a novel geometric invariant which counts singular points with suitable weights.
