Abstract
In this paper, we will introduce the notion of harmonic stability for complete minimal hypersurfaces in a complete Riemannian manifold. The first result we prove, is that a complete harmonic stable minimal surface in a Riemannian manifold with non-negative Ricci curvature is conformally equivalent to either a plane R2 or a cylinder R × S1, which generalizes a theorem due to Fischer-Colbrie and Schoen [12].
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