Communications in Analysis and Geometry

Volume 14 (2006)

Number 4

Liouville-type properties for embedded minimal surfaces

Pages: 703 – 723



William H. Meeks

Joaquín Pérez

Antonio Ros


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 \gt 0.

2010 Mathematics Subject Classification


Published 1 January 2006