Half-space theorems for minimal surfaces in Nil3 and Sol3
Abstract
We prove some half-space theorems for minimal surfaces in the Heisenberg group Nil3 and the Lie group Sol3 endowed with their 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, then S is another special plane.
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