Einstein-Lichnerowicz约束系统的稳定性和不稳定性
Stability and instability of the Einstein-Lichnerowicz constraint system
摘要：
我们调查的相关性的共形方法调查的稳定性问题的爱因斯坦-Lichnerowicz共形约束系统在非线性标量场设置。我们证明了系统的稳定性，相对于任意扰动的通用聚焦物理数据封闭的局部共形平坦的流形，在任何维度。通过构造显式的不稳定性例子，我们还证明了当其假设不满足时，我们的稳定性结果是尖锐的。我们的结果适用于更一般的类约束系统。
英文摘要：
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to arbitrary perturbations of generic focusing physics data on closed locally conformally flat manifolds, in any dimension. We also show that our stability result is sharp by constructing explicit instability examples when its assumptions are not satisfied. Our results apply to a more general class of constraint-like systems.
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