Half-space theorems for minimal surfaces in Nil_3 and Sol_3
Differential Geometry
2013-05-09 v1
Abstract
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.
Cite
@article{arxiv.1005.3963,
title = {Half-space theorems for minimal surfaces in Nil_3 and Sol_3},
author = {Benoit Daniel and William H. Meeks and Harold Rosenberg},
journal= {arXiv preprint arXiv:1005.3963},
year = {2013}
}
Comments
19 pages, 3 figures