de Sitter空间中介于两个平行伪球面之间的类空超曲面

Spacelike Hypersurfaces in S_1^(n+1) Between Two Parallel Hyperbolids

本文利用广义极大原理证明了de Sitter空间中介于两个平行的、同侧的n维伪球面之间的完备常平均曲率类空超曲面一定是伪球面．对于常高阶平均曲率的完备超曲面,当截曲率有下界时,也有相应的唯一性结果．

This paper characterizes the spacelike hyperbolids in de Sitter space S1^n＋1 as the only complete spacelike hypersurfaces with constant mean curvature which are between two parallel hyperbolids in the same side. Under the condition that the sectional curvature is bounded away from below, the same result holds for the complete spacelike hypersurfaces with constant higher mean curvature.