Localized deformation for initial data sets with the dominant energy condition

Justin Corvino Lafayette College Lan-Hsuan Huang University of Connecticut

Geometric Analysis and Geometric Topology mathscidoc:1606.15001

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. Chru\'sciel and E. Delay, with some refined analysis.
dominant energy condition
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@inproceedings{justinlocalized,
  title={Localized deformation for initial data sets with the dominant energy condition},
  author={Justin Corvino, and Lan-Hsuan Huang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160628093011617145040},
}
Justin Corvino, and Lan-Hsuan Huang. Localized deformation for initial data sets with the dominant energy condition. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160628093011617145040.
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