We study, using mean curvature flow methods, $$2+1$$ dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler characteristic and are initially expanding everywhere, then we prove that the spatial slices reach infinite volume, asymptotically converge on average to de Sitter and they become, almost everywhere, physically indistinguishable from de Sitter. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations and the formation of black holes.

中文翻译：

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$$\Lambda >0$$Λ>0 在 $$2+1$$2+1 维度上宇宙学的渐近行为

我们使用平均曲率流方法研究了具有正宇宙常数的 2+1 维宇宙学和满足主要和强能量条件的物质。如果空间切片是紧凑的，具有非正欧拉特征，并且最初到处扩展，那么我们证明空间切片达到无限体积，平均渐近收敛到 de Sitter 并且它们几乎在所有地方都变得与 de Sitter 在物理上无法区分。尽管存在初始任意大的密度波动和黑洞的形成，这仍然适用。