论文标题
Minkowski Space中的整个空间式超曲面，$σ_K$曲率
Entire spacelike hypersurfaces with constant $σ_k$ curvature in Minkowski space
论文作者
论文摘要
在本文中，我们证明了平滑，全部，严格的凸面，恒定的$σ_K$曲率超曲面，在Minkowski空间中具有规定的灯光方向。这相当于证明具有带有规定的高斯映射图像的光滑，全部，严格凸面，固定，固定$σ_K$曲率超出曲面的存在。我们还表明，没有任何完整的，凸面，严格的间距，常数$σ_K$曲率超出曲面。此外，我们将结果概括为\ cite {rwx}，并严格构建凸面，固定，常数$σ_K$曲率超出表面，并具有有限的主曲率，其高斯映射的图像是单位球。
In this paper, we prove the existence of smooth, entire, strictly convex, spacelike, constant $σ_k$ curvature hypersurfaces with prescribed lightlike directions in Minkowski space. This is equivalent to prove the existence of smooth, entire, strictly convex, spacelike, constant $σ_k$ curvature hypersurfaces with prescribed Gauss map image. We also show that there doesn't exist any entire, convex, strictly spacelike, constant $σ_k$ curvature hypersurfaces. Moreover, we generalize the result in \cite{RWX} and construct strictly convex, spacelike, constant $σ_k$ curvature hypersurface with bounded principal curvature, whose image of the Gauss map is the unit ball.
