Journal of Differential Geometry

Null mean curvature flow and outermost MOTS

Theodora Bourni and Kristen Moore

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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.


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

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

Received: 25 February 2015
First available in Project Euclid: 6 February 2019

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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.

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