de Sitter 空间中的常平均曲率完备类空超曲面

设Ｍ是常曲率ｃ的ｄｅ Ｓｉｔｔｅｒ空间Ｓ１＾ｎ＋１（ｃ）的常平均曲率的完备类空超曲面,Ｓ表示第二形式的范数平方。本文证明：差Ｓ〈２√ｎ－１ｃ,则Ｍ是全脐的和等距于一球面。     

在Sn1+1空间中具有常数量曲率的类空超曲面的高斯映射

在这篇文章中,我们研究在de Sitter空间中具有非负常值的第r个平均曲率的紧致的类空超曲面.我们证明了在合适的条件下紧致的类空超曲面是全脐的.     

de Sitter空间中具有常均曲率的类空超曲面

设M是deSitter空间中具有常均曲率的类空超曲面,本文给出M是全脐的或是等参的一些条件．     

On the Curvatures of Complete Spacelike Hypersurfaces in de Sitter Space

We establish some estimates for the higher-order mean curvatures, the scalar curvature and the Ricci curvature of a complete spacelike hypersurface in de Sitter space which is contained in certain unbounded regions of the ambient space. Our results will be an application of a generalized maximum principle due to Omori.     

On the Ricci Curvature of Compact Spacelike Hypersurfaces in de Sitter Space

In this paper we establish a sufficient condition for a compact spacelike hypersurface in de Sitter space to be spherical in terms of a pinching condition for the Ricci curvature. Our result will be a consequence of an integral formula involving the Ricci curvature and the scalar curvature of the hypersurface. We also derive some other consequences and applications of this formula.     

de Sitter空间中具平行平均曲率向量的完备类空子流形(Ⅱ)

本文证明了de Sitter空间中具平行平均曲率向量的完备类空子流形在其第二基本形式模长平方S＜2(n-1c)的平方根时是全脐子流形。     

De Sitter空间中具有非负截曲率的常平均曲率完备类空超曲面

设M为de Sitter空间S1^n 1（1）中的完备（非紧）类空超曲面，具有常平均曲率和非负截曲率，在适当条件下，我们证明了它与欧式空间或者双曲柱面等距。     

de Sitter空间中具有平行中曲率的完备类空子流形的注记

本文纠正了论文“de Sitter空间中具有平行中曲率的完备类空子流形”证明中的一些失误，证明了de Sitter空间中具有平行中曲率的n维完备类空子流形的—个刚性定理．     

On the volume and the Gauss map image of spacelike hypersurfaces in de Sitter space

In this paper we prove that a complete spacelike hypersurface in de Sitter space such that its image under the Gauss map is contained in a hyperbolic geodesic ball of radius is necessarily compact and its -dimensional volume satisfies , where denotes the volume of a unitary round -sphere. We also characterize the case where these inequalities become equalities. As an application of our result, we also conclude that Goddard's conjecture is true under the assumption that the hyperbolic image of the hypersurface is bounded.

     

Complete spacelike hypersurfaces with constant mean curvature in anti-de Sitter space

In this paper, we investigate the complete spacelike hypersurfaces with constant mean curvature and two distinct principal curvatures in an anti-de Sitter space. We give a characterization of hyperbolic cylinder and prove the conjecture in a paper by L. F. Cao and G. X. Wei [J. Math. Anal. Appl., 2007, 329(1): 408–414].     

de Sitter空间中具平行平均曲率向量的完备类空子流形

本文证明了ｄｅＳｉｔｔｅｒ空间中具平行平均曲率向量的完备类空子流形在Ｈ２〉Ｃ时其第二基本形式模长平方是上有界的，从而推广了Ｕ－ＨａｎｇＫＩ＾（４）及Ｑ．Ｍ．Ｃｈｅｎｇ＾（３）中的结果。     

Complete Space－like Submanifolds in a de Sitter Space with Parallel Mean CurvatureVector

ＣｏｍｐｌｅｔｅＳｐａｃｅ－ｌｉｋｅＳｕｂｍａｎｉｆｏｌｄｓｉｎａｄｅＳｉｔｔｅｒＳｐａｃｅｗｉｔｈＰａｒａｌｌｅｌＭｅａｎＣｕｒｖａｔｕｒｅＶｅｃｔｏｒＳｈｕＳｈｉｃｈａｎｇ（ＸｉａｎｙａｎｇＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｘｉａｎｙａｎｇ，７１２...     

三维 Anti-de Sitter空间中常平均曲率旋转曲面

本文主要构造三维 Anti-de Sitter空间中单参数族的常平均曲率旋转曲面.     

Lorentz空间中常平均曲率类空超曲面

本文证明了ｎ＋１维Ｌｏｒｅｎｔｚ空Ｌｎ＋１中以Ｓｎ－１（ｒ）为边界的紧致常平均曲率类空超曲面只有 Ｂｎ（ｒ）和超伪球面盖．对于 Ｒｎ＋１中的紧致常平均曲率超曲面，当高斯映照像落在一个半球面内时，得到相应的唯一性结果．     

GRW时空中具有常$k$阶平均曲率的类空超曲面的高度估计

本文利用广义的Omori-Yau极大值原则,得到了广义的Robertson-Walker(GRW)时空中具有常高阶平均曲率并且边界包含在一slice中的类空超曲面的高度估计.同时利用这些结果得到了一些拓扑方面的结论.最后对拉普拉斯算子和一些椭圆型的微分算子利用Omori-Yau极大值原则,得到了一些更广泛的非存在性的结果.     

Radial Graphs with Constant Mean Curvature in the Hyperbolic Space

The existence is proved of radial graphs with constant mean curvature in the hyperbolic space H ⁿ⁺¹ defined over domains in geodesic spheres of H ⁿ⁺¹ whose boundary has positive mean curvature with respect to the inward orientation.     

Minimizing Constant Mean Curvature Hypersurfaces in Hyperbolic Space

We study the constant mean curvature (CMC) hypersurfaces in whose asymptotic boundaries are closed codimension-1 submanifolds in . We consider CMC hypersurfaces as generalizations of minimal hypersurfaces. We naturally generalize some notions of minimal hypersurfaces like being area-minimizing, convex hull property, exchange roundoff trick to CMC hypersurface context. We also give a generic uniqueness result for CMC hypersurfaces in hyperbolic space.     

De Sitter空间中半对称的类空超曲面

给出了De Sitter空间S1^n 1(1)（n≥3)的类空超英面是半对称的充要条件，决定了S1^n 1(1)（n≥3)的半对称类空超曲面的局部结构，证明了S1^n 1(1)（n≥3)具有常平均曲率的连通完备的半对称类空超曲面或是全脐的，或是具有两上不同主曲率的等参超曲面。     

拟常曲率空间中具有常平均曲率的完备超曲面

主要研究了拟常曲率空间中具有常平均曲率的完备超曲面,得到了这类超曲面全脐的一个结果.即若Nn+1的生成元η∈TM,且a-2|b|=c(常数)>0,则当S<2 n-1~(1/2)(a-2|b|)时,M为全脐超曲面.