论文标题
双曲线空间及其应用
A Mountain-pass Theorem in Hyperbolic Space and its Application
论文作者
论文摘要
我们为双曲线空间中的某些完全最小的超曲面开发了一个最小的理论。特别是，我们表明，给定两个严格稳定的最小超曲面，它们都是渐近的，它们均与相同的理想边界，两者之间存在一个新的。作为一种应用，我们表明在低熵条件下，所有最小的超曲面渐近性渐近性与相同的理想边界都是同位素。
We develop a min-max theory for certain complete minimal hypersurfaces in hyperbolic space. In particular, we show that given two strictly stable minimal hypersurfaces that are both asymptotic to the same ideal boundary, there is a new one trapped between the two. As an application, we show that under a low entropy condition, all the minimal hypersurfaces asymptotic to the same ideal boundary are isotopic.
