On harmonic functions and the hyperbolic metric
Complex Variables
2014-03-06 v3
Abstract
Motivated by some recent results of Kalaj and Vuorinen (Proc. Amer. Math. Soc., 2012), we prove that positive harmonic functions defined in the upper half--plane are contractions w.r.t. hyperbolic metrics of half--plane and positive part of the real line, respectively
Keywords
Cite
@article{arxiv.1307.4006,
title = {On harmonic functions and the hyperbolic metric},
author = {Marijan Markovic},
journal= {arXiv preprint arXiv:1307.4006},
year = {2014}
}