零平均曲率流与最外层MOTS
微分几何
2022-08-16 v2
摘要
我们研究了时空初始数据集中超曲面由其零平均曲率驱动的演化。利用水平集方法发展了弱解理论。从任意平均凸、外未触及超曲面出发，我们证明了存在零平均曲率流的弱解，该弱解作为使用-正则化方法定义的近似解的极限给出。我们证明了近似解在最外层MOTS上爆破，并且弱解（作为有限周长集的边界）收敛到一个广义MOTS。
引用
@article{arxiv.1503.04023,
title = {Null mean curvature flow and outermost MOTS},
author = {Theodora Bourni and Kristen Moore},
journal= {arXiv preprint arXiv:1503.04023},
year = {2022}
}
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