On the stability of the positive mass theorem for asymptotically hyperbolic graphs
On the stability of the positive mass theorem for asymptotically hyperbolic graphs
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渐近双曲图正质量定理的稳定性
DOI：
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发表时间：
2018
影响因子：
0.7
通讯作者：
Armando J. Cabrera Pacheco
中科院分区：
文献类型：
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作者：
Armando J. Cabrera Pacheco
正质量定理指出，具有非负数量曲率的完备渐近平坦流形的总质量是非负的；此外，当且仅当流形与欧氏空间等距时，总质量等于零。Huang和Lee(Commun Math Phys337(1)：151-169,2015)证明了一类具有非负标量曲率的n维渐近平坦图(n≥3\DocumentClass[12pt]{Minimum}\Usepackage{amsath}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{matrsfs}\usepackage{upgreek}\setlong{\odsidemargin}{-69pt}\Begin{Document}$n\Ge 3$\end{Document})的正质量定理的稳定性。由他们的工作和使用Dahl等人的结果激励。(Ann Henri Poincaré14(5)：1135-1168,2013)，我们采用他们的想法，得到了关于正质量定理在电流意义下的稳定性的类似结果，对于一类n维(n≥3)\DocumentClass[12pt]{Minimum}\USIPACKAGE{amsath}\UsPACKAGE{WASYSYM}\USIPACKAGE{amsFonts}\USIPPACKAGE{amssymb}\USIPPACKAGE{MARTHROSF}\USIPPACKAGE{upgreek}\setLength{\oddsidemargin}{-69pt}\Begin{Document}$$(n\ge 3)$$\end{Document}渐近双曲图，其标量曲率大于或等于-n(n-1)\DocumentClass[12pt]{\}Usepackage{amsath}\usepackage{wa ysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$-\，N(n-1)$$\end{文档}。
The positive mass theorem states that the total mass of a complete asymptotically flat manifold with nonnegative scalar curvature is nonnegative; moreover, the total mass equals zero if and only if the manifold is isometric to the Euclidean space. Huang and Lee (Commun Math Phys 337(1):151–169, 2015) proved the stability of the positive mass theorem for a class of n-dimensional (n≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \ge 3$$\end{document}) asymptotically flat graphs with nonnegative scalar curvature, in the sense of currents. Motivated by their work and using results of Dahl et al. (Ann Henri Poincaré 14(5):1135–1168, 2013), we adapt their ideas to obtain a similar result regarding the stability of the positive mass theorem, in the sense of currents, for a class of n-dimensional (n≥3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n \ge 3)$$\end{document} asymptotically hyperbolic graphs with scalar curvature bigger than or equal to -n(n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\,n(n-1)$$\end{document}.
关于渐近双曲流形的质量方面函数和正能量定理
影响因子：
3.5
作者：
Chruściel, Piotr T;Galloway, Gregory J;Nguyen, Luc;Paetz, Tim-Torben
通讯作者：
Paetz, Tim-Torben