Half-space theorems for minimal surfaces in Nil_3 and Sol_3

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

2010-05-21

arxiv.org/abs/1005.3963v1

Mathematics

Differential Geometry

19 pages, 3 figures

Scientific paper

We prove some half-space theorems for minimal surfaces in the Heisenberg group Nil_3 and the Lie group Sol_3 endowed with their left-invariant Riemannian metrics. If S is a properly immersed minimal surface in Nil_3 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 Sol_3 that lies on one side of a special plane, then S is another special plane.

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