Communications in Analysis and Geometry
Volume 14 (2006)
Liouville-type properties for embedded minimal surfaces
Pages: 703 – 723
In this paper, we study conformal properties of complete embedded minimal surfaces in flat three-manifolds. These properties include recurrence, transience and the existence/nonexistence of nonconstant bounded and/or positive harmonic functions. We also apply these results to study the question of existence of complete embedded minimal surfaces which are a-stable for some a > 0.
2010 Mathematics Subject Classification