This paper looks at the splitting problem for globally hyperbolic spacetimes with timelike Ricci curvature bounded below containing a (spacelike, acausal, future causally complete) hypersurface with mean curvature bounded from above. For such spacetimes we show a splitting theorem under the assumption of either the existence of a ray of maximal length or a maximality condition on the volume of Lorentzian distance balls over the hypersurface. The proof of the first case follows work by Andersson, Galloway and Howard and uses their geometric maximum principle for level sets of the (Lorentzian) Busemann function. For the second case we give a more elementary proof.

中文翻译：

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洛伦兹流形中超曲面的分裂定理

本文着眼于全局双曲时空的分裂问题，类时 Ricci 曲率限定在下方，包含一个（类空间、非因果、未来因果完整）超曲面，平均曲率从上方限定。对于这样的时空，我们在假设存在最大长度的射线或超曲面上洛伦兹距离球体积的最大值条件下展示分裂定理。第一种情况的证明遵循 Andersson、Galloway 和 Howard 的工作，并将他们的几何最大值原理用于（Lorentzian）Busemann 函数的水平集。对于第二种情况，我们给出更基本的证明。