Height Estimates for Spacelike Hypersurfaces with Constant $k$-Mean Curvature in GRW Spacetimes
Received:September 05, 2016  Revised:December 09, 2016
Key Word: height estimates   generalized Robertson-Walker spacetimes   spacelike hypersurface   higher order mean curvature  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11371076).
Author NameAffiliation
Ximin LIU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Ning ZHANG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.05.001
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