## Journal of Differential Geometry

### 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 $\partial \Omega$, 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.

#### Note

Part of this work was completed while the second named author was financed by the Sonderforschungsbereich #ME3816/1-1 of the DFG.

#### Article information

Source
J. Differential Geom., Volume 111, Number 2 (2019), 191-239.

Dates
First available in Project Euclid: 6 February 2019

https://projecteuclid.org/euclid.jdg/1549422101

Digital Object Identifier
doi:10.4310/jdg/1549422101

Mathematical Reviews number (MathSciNet)
MR3909907

Zentralblatt MATH identifier
07015569

#### Citation

Bourni, Theodora; Moore, Kristen. Null mean curvature flow and outermost MOTS. J. Differential Geom. 111 (2019), no. 2, 191--239. doi:10.4310/jdg/1549422101. https://projecteuclid.org/euclid.jdg/1549422101