A Note on Harmonic Functions on surfaces
Analysis of PDEs
2014-08-15 v2
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.
Cite
@article{arxiv.1405.0944,
title = {A Note on Harmonic Functions on surfaces},
author = {Jean C. Cortissoz},
journal= {arXiv preprint arXiv:1405.0944},
year = {2014}
}
Comments
Comments and corrections are very welcome! Mistakes and typos found in a previous version have been corrected