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arXiv 1503.04023math.DG
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中曲率流与最外层MOTS

Null mean curvature flow and outermost MOTS

Theodora Bourni, Kristen Moore

备注：
A mistake in the use of the L^1 norm of the mean curvature instead of the L^2 norm in proofs of Theorems 37 and 39 was corrected. The use of the L^2 norm is needed in the application of the varifold convergence
发表信息：
J. Differential Geom. 111(2): 191-239 (February 2019)
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摘要：

我们利用超曲面的零中曲率研究了超曲面在时空初始数据集中的演化。利用水平集方法建立了一个弱解理论。从一个任意平均凸，外未挖掘超曲面$\partialΩ_0$，我们表明，存在一个弱解的零中曲率流，给出了一个限制的近似解，使用$\varepsilon$ -正则化方法定义。我们证明了该问题的近似解在最外层MOTS上爆破，而弱解收敛（作为有限周长集的边界）到广义MOTS。

英文摘要：

We study the evolution of hypersurfaces in spacetime initial data sets by their null mean curvature. A theory of weak solutions is developed using the level-set approach. Starting from an arbitrary mean convex, outer untapped hypersurface $\partialΩ_0$, we show that there exists a weak solution to the null mean curvature flow, given as a limit of approximate solutions that are defined using the $\varepsilon$-regularization method. We show that the approximate solutions blow up on the outermost MOTS and the weak solution converges (as boundaries of finite perimeter sets) to a generalized MOTS.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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