We consider open globally hyperbolic spacetimes $N$ of dimension $n + 1, n \geq 3$, which are spatially asymptotic to a Robertson–Walker spacetime or an open Friedmann universe with spatial curvature $\tilde{\kappa} = 0, -1$ and prove, under reasonable assumptions, that there exists a unique foliation by spacelike hypersurfaces of constant mean curvature and that the mean curvature function $\tau$ is a smooth time function if $N$ is smooth. Moreover, among the Friedmann universes which satisfy the necessary conditions are those that reflect the present assumptions of the development of the universe.

中文翻译：

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CMC的开放时空渐近线向开放的Robertson-Walker时空

我们考虑维度为$ n + 1，n \ geq 3 $的开放双曲时空$ N $，它们在空间上渐近于Robertson-Walker时空或具有空间曲率$ \ tilde {\ kappa = 0的开放Friedman宇宙-1 $并证明，在合理的假设下，具有恒定平均曲率的类似空间的超曲面存在唯一的叶状结构，并且如果$ N $是光滑的，则平均曲率函数$ \ tau $是光滑的时间函数。此外，在满足必要条件的弗里德曼宇宙中，有一些反映了当前宇宙发展的假设。