A Note on Harmonic Functions on surfaces
arXiv:1405.0944
Abstract
We review and give elementary proofs of Liouville type properties of harmonic and subharmonic functions in the plane endowed with a complete Riemannian metric, and prove a gap theorem for the possible growth of harmonic functions when this metric has nonnegative Gaussian curvature.
Comments and corrections are very welcome! Mistakes and typos found in a previous version have been corrected