Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space
Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space
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欧氏空间图超曲面拟局部正质量定理的稳定性
DOI：
10.1090/tran/8297
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发表时间：
2019
影响因子：
1.3
通讯作者：
Stephen McCormick
中科院分区：
文献类型：
--
作者：
Aghil Alaee;Armando J. Cabrera Pacheco;Stephen McCormick
我们给出了正质量定理稳定性的一个准局部版本。我们处理Brown-York准局部质量，因为它具有正性和刚性，因此可以研究这个刚性声明的稳定性。具体地说，我们问，如果某个紧致流形的边界的Brown-York质量接近于零，那么在某种意义上，该流形是否必须接近欧几里得区域？
在这里，我们考虑了一类具有边界的紧致$n$-流形，它可以在$\mathbb{R}^{n+1}中实现为图，并建立了如下结论。如果这种紧致流形的边界的Brown-York质量很小，则该流形相对于Federer-Fleming平坦距离接近欧几里得超平面。
We present a quasi-local version of the stability of the positive mass theorem. We work with the Brown--York quasi-local mass as it possesses positivity and rigidity properties, and therefore the stability of this rigidity statement can be studied. Specifically, we ask if the Brown--York mass of the boundary of some compact manifold is close to zero, must the manifold be close to a Euclidean domain in some sense?
Here we consider a class of compact $n$-manifolds with boundary that can be realized as graphs in $\mathbb{R}^{n+1}$, and establish the following. If the Brown--York mass of the boundary of such a compact manifold is small, then the manifold is close to a Euclidean hyperplane with respect to the Federer--Fleming flat distance.
具有几乎非负标量曲率的图形环面的稳定性
DOI：
10.1007/s00526-020-01790-w
发表时间：
2020
影响因子：
2.1
作者：
Armando J. Cabrera Pacheco;Christian Ketterer;Raquel Perales
通讯作者：
Raquel Perales