摘要
本文给出了双曲空间H^n中旋转对称的极小超曲面的微分方程,对这类超曲面进行了分类,它们是H^n中的超平面或广义悬链面,而每个广义悬链面被夹在两个平行的超平面之间,且以这两个超平面为渐近平面.
Let M be a rotational minimal hypersurface in the hyperbolic space Hn. In this paper, we give differential equation of the generating curve y in the fundamental domain H2+, and obtain the following clossification theorem.Theorem The rotational minimal hypersurfaces in the hyperbolic space Hn muse be hyperplane or generalized catenoids. Moreover, each generalized cat-enoid is bounded between two parallel hyperplanes and is asymptotic them.
