论文标题
半空间定理，$ \ mathbb {h}^3 $的$ 1 $ -Surfaces
Half-space theorems for $1$-surfaces of $\mathbb{H}^3$
论文作者
论文摘要
在本文中，我们调查了$ 1 $ surfaces的交叉问题，沉浸在一个完整的三曼尼亚三体manifold $ p $中，而RICCI曲率从下面限制为$ -2 $。我们首先以$ 1 $ -Surfaces的形式证明了Frankel's Type定理，当$ \ text {\ rm ric} _ {p}> -2 $时，将有界曲率浸入$ p $。在这种情况下，我们还提供了一个标准，以确定完整的$ 1 $ -SURFACE是否合适。当实现$ 1 $ -surfaces之间的距离时，即使$ \ text {\ rm ric} _ {p} \ geq -2 $，也会建立分裂结果。在双曲空间$ \ mathbb {h}^3 $中，我们显示出强的半空间定理，用于具有有界曲率的完整$ 1 $ surfaces类，抛物线质量$ 1 $ - surfaces，以及随机完整的$ h $ -Surfaces，带有$ h <1 $。作为我们技术的副产品，Infinity的最大原理以$ 1 $ -SURFACES的$ \ MATHBB {H}^3给出。$
In this paper we investigate the intersection problem for $1$-surfaces immersed in a complete Riemannian three-manifold $P$ with Ricci curvature bounded from below by $-2$. We first prove a Frankel's type theorem for $1$-surfaces with bounded curvature immersed in $P$ when $\text{\rm Ric}_{P} > -2$. In this setting we also give a criterion for deciding whether a complete $1$-surface is proper. A splitting result is established when the distance between the $1$-surfaces is realized, even if $\text{\rm Ric}_{P} \geq -2$. In the hyperbolic space $\mathbb{H}^3$ we show strong half-space theorems for the classes of complete $1$-surfaces with bounded curvature, parabolic $1$-surfaces, and stochastically complete $H$-surfaces with $H<1$. As a by-product of our techniques a Maximum Principle at Infinity is given for $1$-surfaces in $\mathbb{H}^3.$
