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Mass angular momentum inequality for axisymmetric vacuum data with small trace

Xin Zhou Department of Mathematics, Stanford University

Differential Geometry mathscidoc:1610.10034

Communication in Analysis and Geometry, 22, (3), 519-571, 2014
In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then a perturbation method is used to solve the maximal surface equation in the spacetime under certain growing condition at infinity. When the initial data set is axisymmetric, we get an axisymmetric maximal graph with the same ADM mass and angular momentum as the given data. The inequality follows from the known results\cite{D1}\cite{ChrusLiWe}\cite{SZ} about the maximal graph.
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[ Download ] [ 2016-10-10 16:38:07 uploaded by xinzhou02 ] [ 1005 downloads ] [ 0 comments ] [ Cited by 4 ] 
@inproceedings{xin2014mass,
  title={Mass angular momentum inequality for axisymmetric vacuum data with small trace},
  author={Xin Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161010163808002710113},
  booktitle={ Communication in Analysis and Geometry},
  volume={22},
  number={3},
  pages={519-571},
  year={2014},
}
Xin Zhou. Mass angular momentum inequality for axisymmetric vacuum data with small trace. 2014. Vol. 22. In Communication in Analysis and Geometry. pp.519-571. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161010163808002710113.
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