论文标题
非紧凑型太空般的考奇高空的规定平均曲率流动
Prescribed mean curvature flow of non-compact space-like Cauchy hypersurfaces
论文作者
论文摘要
在本文中，我们考虑了在广义的Robertson-Walker时空中，有界几何形状的非紧密空间曲面的规定平均曲率流。我们证明该流量保留了空间的条件并存在于无限的时间。我们还证明了在具有边界的歧管的环境中融合。我们的讨论概括了Ecker，Huisken，Gerhardt和其他有关关键方面的工作：我们考虑在有界几何形状的假设下考虑任何非紧凑的Cauchy Hypersurface。此外，我们通过考虑配备有特定类别的扭曲产品指标的全球劳伦斯空间时间来专注于上述作品。
In this paper we consider the prescribed mean curvature flow of a non-compact space-like Cauchy hypersurface of bounded geometry in a generalized Robertson-Walker space-time. We prove that the flow preserves the space-likeness condition and exists for infinite time. We also prove convergence in the setting of manifolds with boundary. Our discussion generalizes previous work by Ecker, Huisken, Gerhardt and others with respect to a crucial aspects: we consider any non-compact Cauchy hypersurface under the assumption of bounded geometry. Moreover, we specialize the aforementioned works by considering globally hyperbolic Lorentzian space-times equipped with a specific class of warped product metrics.
