论文标题
维度8中通用指标的最小曲面
Minimal hypersurfaces for generic metrics in dimension 8
论文作者
论文摘要
我们表明，在带有$ c^\ infty $ generic指标的$ 8 $维封闭式riemmanian歧管中，每个最小的超曲面都是光滑且非高度的。这证实了在第八维中最小的超曲面的完全普通猜想。这也使我们能够概括（Almgren-Pitts）Min-Max最小超曲面的许多通用几何特性，以前仅在低维度中已知，以降低尺寸八。
We show that in an $8$-dimensional closed Riemmanian manifold with $C^\infty$-generic metrics, every minimal hypersurface is smooth and nondegenerate. This confirms a full generic regularity conjecture of minimal hypersurfaces in dimension eight. This also enables us to generalize many generic geometric properties of (Almgren-Pitts) min-max minimal hypersurfaces, previously only known in low dimensions, to dimension eight.
