能量占优条件下初始数据集的局部变形
Localized deformation for initial data sets with the dominant energy condition
摘要：
我们考虑具有主导能量条件的爱因斯坦场方程的初始数据集的局部变形。对于弱不等式的变形结果需要进行细致的处理。我们引入了一个修正的约束算子来吸收主导能量条件下度量的一阶变化。通过建立局部满射性定理，利用紧支集变分将优势能量条件推广为严格不等式，得到了优势能量条件下的新的胶合结果.局部满射性的证明是对第一作者和R. Schoen和P.延迟，一些精细的分析。
英文摘要：
We consider localized deformation for initial data sets of the Einstein field equations with the dominant energy condition. Deformation results with the weak inequality need to be handled delicately. We introduce a modified constraint operator to absorb the first order change of the metric in the dominant energy condition. By establishing the local surjectivity theorem, we can promote the dominant energy condition to the strict inequality by compactly supported variations and obtain new gluing results with the dominant energy condition. The proof of local surjectivity is a modification of the earlier work for the usual constraint map by the first named author and R. Schoen and by P. Chruściel and E. Delay, with some refined analysis.
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