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February 2019 Null mean curvature flow and outermost MOTS
Theodora Bourni, Kristen Moore
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J. Differential Geom. 111(2): 191-239 (February 2019). DOI: 10.4310/jdg/1549422101

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.

Funding Statement

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

Citation

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Theodora Bourni. Kristen Moore. "Null mean curvature flow and outermost MOTS." J. Differential Geom. 111 (2) 191 - 239, February 2019. https://doi.org/10.4310/jdg/1549422101

Information

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

zbMATH: 07015569
MathSciNet: MR3909907
Digital Object Identifier: 10.4310/jdg/1549422101

Rights: Copyright © 2019 Lehigh University

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Vol.111 • No. 2 • February 2019
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