Blowup rate control for solution of Jang’s equation and its application to Penrose inequality

We prove that the blowup term of a blowup solution of Jang’s equation on an initial data set $(\mathcal{M}, g, k)$ near an arbitrary strictly stable MOTS $\Sigma$ is exactly $-\frac{1}{\sqrt{\lambda}} \log \tau$, where $\tau$ is the distance from $\Sigma$ and $\lambda$ is the principal eigenvalue of the MOTS stability operator of $\Sigma$. We also prove that the gradient of the solution is of order $\tau^{-1}$. Moreover, we apply these results to get a Penrose-like inequality under additional assumptions.

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Published 30 August 2023