论文标题
Minkowski Space中的整个空间式高空曲面，$σ_{N-1} $曲率
Entire spacelike hypersurfaces with constant $σ_{n-1}$ curvature in Minkowski space
论文作者
论文摘要
我们证明，在Minkowski Space中，如果空间般的$（N-1）$ - 凸出hypersurface $ m $，带有常数$σ_{n-1} $曲率具有有限的主曲线，则$ m $ is isvex。此外，如果$ m $不是严格凸出的，则在$ \ mathbb {r}^{n，1} $刚性动作后，$ m $将作为产品$ m^{n-1} \ times \ times \ times \ mathbb {r}。有限的主曲线。
We prove that, in Minkowski space, if a spacelike, $(n-1)$-convex hypersurface $M$ with constant $σ_{n-1}$ curvature has bounded principal curvatures, then $M$ is convex. Moreover, if $M$ is not strictly convex, after an $\mathbb{R}^{n,1}$ rigid motion, $M$ splits as a product $M^{n-1}\times\mathbb{R}.$ We also construct nontrivial examples of strictly convex, spacelike hypersurface $M$ with constant $σ_{n-1}$ curvature and bounded principal curvatures.
