论文标题
点的固有平坦收敛和对正质量定理稳定性的应用
Intrinsic flat convergence of points and applications to stability of the positive mass theorem
论文作者
论文摘要
我们证明了点的固有平面收敛的结果--- Sormani在\ cite {sormani-aa}中首先探索的概念。特别是，我们讨论了与Gromov-Hausdorff积分收敛的兼容性--- Gromov在\ cite {gromov-poly}中首先描述的概念。 我们将这些结果应用于数学相对性中正质量定理的稳定性问题。具体而言，我们为欧几里得空间的图形高度曲面而对本质的平坦稳定性进行了重新访问\ cite {hls}：我们能够在\ cite {hls}的\ cite {hls}的定理证明中填写一些细节。此外，鉴于\ cite {hls}的定理〜1.3证明中的公认错误，我们提供了一个替代证明，以扩展\ cite {ap20}的最新工作。
We prove results on intrinsic flat convergence of points---a concept first explored by Sormani in \cite{Sormani-AA}. In particular, we discuss compatibility with Gromov-Hausdorff convergence of points---a concept first described by Gromov in \cite{Gromov-poly}. We apply these results to the problem of stability of the positive mass theorem in mathematical relativity. Specifically, we revisit the article \cite{HLS} on intrinsic flat stability for the case of graphical hypersurfaces of Euclidean space: We are able to fill in some details in the proofs of Theorems 1.4 and Lemma~5.1 of \cite{HLS} and strengthen some statements. Moreover, in light of an acknowledged error in the proof of Theorem~1.3 of \cite{HLS}, we provide an alternative proof that extends recent work of \cite{AP20}.
