GRW时空中具有常$k$阶平均曲率的类空超曲面的高度估计

Height Estimates for Spacelike Hypersurfaces with Constant $k$-Mean Curvature in GRW Spacetimes

中文关键词:  高度估计  广义的Robertson-Walker时空  类空超曲面  高阶平均曲率.

英文关键词:height estimates  generalized Robertson-Walker spacetimes  spacelike hypersurface  higher order mean curvature

中文摘要:

      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.

英文摘要:

      In this paper, using the generalized Omori-Yau maximum principle, we obtain height estimates for spacelike hypersurface in a generalized Robertson-Walker (GRW) spacetime with constant higher order mean curvature and whose boundary is contained in a slice. Furthermore, we apply these results to draw some topological conclusions. Finally, considering the Omori-Yau maximum principle for the Laplacian and for more general elliptic trace type differential operators, we have some further non-existence results.