Blowup of Jang's equation at outermost marginally trapped surfaces

Metzger, Jan

doi:10.1007/s00220-009-0934-x

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Blowup of Jang's equation at outermost marginally trapped surfaces

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Metzger, Jan
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0711.4753v1.pdf
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CMP294_61.pdf
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Citation

Metzger, J. (2010). Blowup of Jang's equation at outermost marginally trapped surfaces. Communications in Mathematical Physics, 294, 61-72. doi:10.1007/s00220-009-0934-x.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5FEC-6

Abstract

The aim of this paper is to collect some facts about the blowup of Jang's equation. First, we discuss how to construct solutions that blow up at an outermost MOTS. Second, we exclude the possibility that there are extra blowup surfaces in data sets with non-positive mean curvature. Then we investigate the rate of convergence of the blowup to a cylinder near a strictly stable MOTS and show exponential convergence near a strictly stable MOTS.