Inverse mean curvature flow and the stability of the positive mass theorem

We study the stability of the Positive Mass Theorem (PMT) in the case where a sequence of regions of manifolds with positive scalar curvature $U^i_T \subset M^3_i$ are foliated by a smooth solution to Inverse Mean Curvature Flow (IMCF) which may not be uniformly controlled near the boundary. Then if $\partial U^i_T = \sum^i_0 \cup \sum^i_t , m_H (\sum^i_t) \to 0$ and extra technical conditions are satisfied we show that $U^i_T$ converges to a flat annulus with respect to Sormani–Wenger Intrinsic Flat (SWIF) convergence.

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Received 11 August 2018

Accepted 14 December 2021

Published 13 August 2024