论文标题
自由边界最小的超曲面
Free boundary minimal hypersurfaces outside of the ball
论文作者
论文摘要
在本文中，我们在欧几里得空间中获得了两种自由边界最小超曲面（简称外部FBMH）的分类定理。第一个结果指出，唯一具有平行嵌入规则末端的外部稳定FBMH是伴奏性超曲面。为了实现这一目标，我们证明了jacobi在$ \ mathbb {r}^{n+1} $中的常规最小末端的bôcher类型结果，经过一些计算，这意味着第一个定理。第二个定理指出，任何带有常规端的外部FBMH $σ$都是catenoidal hypersurface。它的证明基于类似于R. Schoen [14]的对称过程。我们还完整地描述了相关性超曲面，包括计算其指数。
In this paper we obtain two classification theorems for free boundary minimal hypersurfaces outside of the unit ball (exterior FBMH for short) in Euclidean space. The first result states that the only exterior stable FBMH with parallel embedded regular ends are the catenoidal hypersurfaces. To achieve this we prove a Bôcher type result for positive Jacobi functions on regular minimal ends in $\mathbb{R}^{n+1}$ which, after some calculations, implies the first theorem. The second theorem states that any exterior FBMH $Σ$ with one regular end is a catenoidal hypersurface. Its proof is based on a symmetrization procedure similar to R. Schoen [14]. We also give a complete description of the catenoidal hypersurfaces, including the calculation of their indices.
