Null mean curvature flow and outermost MOTS
Abstract
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 , 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 -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.
Cite
@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}
}
Comments
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