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arXiv · 1807.08822

Inverse Mean Curvature Flow and the Stability of the Positive Mass Theorem

Brian Allen
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Abstract

We study the stability of the Positive Mass Theorem (PMT) in the case where a sequence of regions of manifolds with positive scalar curvature $U_T^i\subset M_i^3$ are foliated by a smooth solution to Inverse Mean Curvature Flow (IMCF) which may not be uniformly controlled near the boundary. Then if $\partial U_T^i = \Sigma_0^i \cup \Sigma_T^i$, $m_H(\Sigma_T^i) \rightarrow 0$ and extra technical conditions are satisfied we show that $U_T^i$ converges to a flat annulus with respect to Sormani-Wenger Intrinsic Flat (SWIF) convergence.

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Brian Allen. 2018-07-23. Inverse Mean Curvature Flow and the Stability of the Positive Mass Theorem. https://arxiv.org/abs/1807.08822

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