Far-from-constant mean curvature solutions of Einstein's constraint equations with positive Yamabe metrics.
Far-from-constant mean curvature solutions of Einstein's constraint equations with positive Yamabe metrics.
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具有正 Yamabe 度量的爱因斯坦约束方程的远非恒定平均曲率解。
DOI：
10.1103/physrevlett.100.161101
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发表时间：
2008
影响因子：
8.6
通讯作者：
G. Tsogtgerel
中科院分区：
文献类型：
--
作者：
M. Holst;G. Nagy;G. Tsogtgerel
我们建立了任意远离常数的平均外在曲率的爱因斯坦约束方程的新的存在性结果。结果适用于正Yamabe类中重新缩放的背景度量，其中数据的可自由指定部分足够小，并且物质能量密度不等于零。两项技术进步使这些结果成为可能：一种新的拓扑不动点论点，在平均外在曲率的空间导数上没有小条件，以及一种新的哈密顿约束的全局超解构造，同样不存在这些条件。结果不仅适用于闭流形上的强解，也适用于弱解和紧流形上的边界。这些结果显然是第一个不需要平均外在曲率空间导数的小条件的结果。
We establish new existence results for the Einstein constraint equations for mean extrinsic curvature arbitrarily far from constant. The results hold for rescaled background metric in the positive Yamabe class, with freely specifiable parts of the data sufficiently small, and with matter energy density not identically zero. Two technical advances make these results possible: A new topological fixed-point argument without smallness conditions on spatial derivatives of the mean extrinsic curvature, and a new global supersolution construction for the Hamiltonian constraint that is similarly free of such conditions. The results are presented for strong solutions on closed manifolds, but also hold for weak solutions and for compact manifolds with boundary. These results are apparently the first that do not require smallness conditions on spatial derivatives of the mean extrinsic curvature.