论文标题
弗兰克尔（Frankel
Frankel's property for free boundary minimal hypersurfaces in the Riemannian Schwarzschild manifolds
论文作者
论文摘要
我们研究了Schwarzschild $ n $ -Manifolds中最小的超曲面的行为，该行为沿边界正交相交。我们表明，当在有界区域中实现它们之间的距离时，自由边界最小的超曲面和完全测量的超平面必须相交。我们还讨论了Schwarzschild指标的何时扰动，其标态曲率不再是正面的。
We study the behavior of minimal hypersurfaces in the Schwarzschild $n$-manifolds that intersect the horizon orthogonally along the boundary. We show that a free boundary minimal hypersurface and a totally geodesic hyperplane must intersect when the distance between them is achieved in a bounded region. We also discuss when the Schwarzschild metric is perturbed in a way that its scalar curvature is no longer positive.
