Communications in Analysis and Geometry

Volume 14 (2006)

Number 4

Liouville-type properties for embedded minimal surfaces

Pages: 703 – 723

DOI: http://dx.doi.org/10.4310/CAG.2006.v14.n4.a5

Authors

William H. Meeks

Joaquín Pérez

Antonio Ros

Abstract

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

53A10

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