反新曲率流与正质量定理的稳定性

Pub Date : 2024-07-29 DOI:10.4310/cag.2023.v31.n10.a5

Allen,Brian

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引用次数: 0

摘要

我们研究了正质量定理（PMT）在以下情况下的稳定性：具有正标量曲率 $U_{T}^{i}\subset M_{i}^{3}$ 的流形区域序列被反平均曲率流（IMCF）的光滑解所叶状化，而反平均曲率流在边界附近可能不是均匀受控的。那么，如果 $partial U_{T}^{i} = \Sigma _{0}^{i}\cup \Sigma _{T}^{i}$，$m_{H}(\Sigma _{T}^{i})\rightarrow 0$，并且满足额外的技术条件，我们就能证明 $U_{T}^{i}$ 收敛到一个与索马尼-温格内在平坦（SWIF）有关的平坦环面。

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Inverse nean 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 $U_{T}^{i}\subset M_{i}^{3}$ 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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