Entire spacelike hypersurfaces with constant $$sigma _k$$ curvature in Minkowski space
Entire spacelike hypersurfaces with constant $$sigma _k$$ curvature in Minkowski space
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闵可夫斯基空间中具有恒定 Ïk 曲率的整个类空间超曲面
DOI：
10.1007/s00208-021-02317-0
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发表时间：
2022
影响因子：
1.4
通讯作者：
Ling Xiao
中科院分区：
文献类型：
--
作者：
Zhizhang Wang;Ling Xiao
本文证明了Minkowski空间中具有规定类光方向的光滑、整、严格凸、类空、常曲率超曲面的存在性。这等价于证明了具有给定高斯映射像的光滑、整、严格凸、类空、常曲率超曲面的存在性。我们还证明了不存在任何整的、凸的、严格类空的、常曲率的超曲面。此外，我们推广了Ren等人（在Minkowski空间中具有常曲率的整类空超曲面。预印本， arXiv：2005.06109 ），构造了主曲率有界的严格凸、类空、常曲率超曲面，其高斯映射的像是单位球.
In this paper, we prove the existence of smooth, entire, strictly convex, spacelike, constantcurvature hypersurfaces with prescribed lightlike directions in Minkowski space. This is equivalent to prove the existence of smooth, entire, strictly convex, spacelike, constantcurvature hypersurfaces with prescribed Gauss map image. We also show that there doesn’t exist any entire, convex, strictly spacelike, constantcurvature hypersurfaces. Moreover, we generalize the result in Ren et al. (Entire spacelike hypersufaces with constantcurvature in Minkowski space. Preprint, arXiv:2005.06109 ) and construct strictly convex, spacelike, constantcurvature hypersurface with bounded principal curvature, whose image of the Gauss map is the unit ball.