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The plateau problem for marginally outer trapped surfaces

Michael Eichmair Massachusetts Institute of Technology

Differential Geometry mathscidoc:1609.10149

Journal of Differential Geometry, 83, (3), 551-583, 2009
We solve the Plateau problem for marginally outer trapped surfaces in general Cauchy data sets. We employ the Perron method and tools from geometric measure theory to force and control a blow-up of Jang’s equation. Substantial new geometric insights regarding the lower order properties of marginally outer trapped surfaces are gained in the process. The techniques developed in this paper are flexible and can be adapted to other non-variational existence problems.
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@inproceedings{michael2009the,
  title={THE PLATEAU PROBLEM FOR MARGINALLY OUTER TRAPPED SURFACES},
  author={Michael Eichmair},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911203112694537806},
  booktitle={Journal of Differential Geometry},
  volume={83},
  number={3},
  pages={551-583},
  year={2009},
}
Michael Eichmair. THE PLATEAU PROBLEM FOR MARGINALLY OUTER TRAPPED SURFACES. 2009. Vol. 83. In Journal of Differential Geometry. pp.551-583. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911203112694537806.
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