Blowup of Jang's equation at outermost marginally trapped surfaces

Understand

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.