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Half-space theorems for minimal surfaces in $Nil_3$ and $Sol_3$

Benoıt Daniel, Universit´e Paris-Est William H. Meeks, University of Massachusetts Harold Rosenberg Instituto Nacional de Matem´atica Pura e Aplicada

Differential Geometry mathscidoc:1609.10218

Journal of Differential Geometry, 88, (1), 41-59, 2011
We prove some half-space theorems for minimal surfaces in the Heisenberg group Nil3 and the Lie group Sol3 endowed with their standard left-invariant Riemannian metrics. If S is a properly immersed minimal surface in Nil3 that lies on one side of some entire minimal graph G, then S is the image of G by a vertical translation. If S is a properly immersed minimal surface in Sol3 that lies on one side of a special plane Et (see the discussion just before Theorem 1.5 for the definition of a special plane in Sol3), then S is the special plane Eu for some u 2 R.
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@inproceedings{benoıt2011half-space,
  title={Half-space theorems for minimal surfaces in $Nil_3$ and $Sol_3$},
  author={Benoıt Daniel,, William H. Meeks,, and Harold Rosenberg},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160912074158885189877},
  booktitle={Journal of Differential Geometry},
  volume={88},
  number={1},
  pages={41-59},
  year={2011},
}
Benoıt Daniel,, William H. Meeks,, and Harold Rosenberg. Half-space theorems for minimal surfaces in $Nil_3$ and $Sol_3$. 2011. Vol. 88. In Journal of Differential Geometry. pp.41-59. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160912074158885189877.
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