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Convexity of reduced energy and mass angular momentum inequalities

Richard Schoen Department of Mathematics, Stanford University Xin Zhou Department of Mathematics, Stanford University

Differential Geometry mathscidoc:1610.10035

Annales Henri Poincare, 14, 1747-1773., 2013
In this paper, we extend the work in \cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic conditions on the second fundamental form, and we also give an $L^{6}-$norm bound for the difference between general data and Extreme Kerr data or Extreme Kerr-Newman data by proving convexity of the renormalized Dirichlet energy when the target has non-positive curvature. In particular, we give the first proof of the strict mass/angular momentum/charge inequality for axisymmetric Einstein/Maxwell data which is not identical with the extreme Kerr-Newman solution.
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[ Download ] [ 2016-10-10 16:44:15 uploaded by xinzhou02 ] [ 764 downloads ] [ 0 comments ] [ Cited by 11 ] 
@inproceedings{richard2013convexity,
  title={Convexity of reduced energy and mass angular momentum inequalities },
  author={Richard Schoen, and Xin Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161010164415543638114},
  booktitle={Annales Henri Poincare},
  volume={14},
  pages={1747-1773.},
  year={2013},
}
Richard Schoen, and Xin Zhou. Convexity of reduced energy and mass angular momentum inequalities . 2013. Vol. 14. In Annales Henri Poincare. pp.1747-1773.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161010164415543638114.
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