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 $\partial {\Omega }_0$, 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 $\epsilon$-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.

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

References in corpus (1)

• Evolving hypersurfaces by their inverse null mean curvature

Cited by in corpus (2)

• The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting
• Mean curvature flow in null hypersurfaces and the detection of MOTS