Lower and upper order of harmonic mappings
Complex Variables
2021-07-06 v1
Abstract
In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in . We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some consequences of a function having finite upper order. In addition, we improve a related result in the case when there is equality in a known distortion theorem for harmonic mappings with finite upper order. Some examples are provided to illustrate the developed theory.
Cite
@article{arxiv.2107.01756,
title = {Lower and upper order of harmonic mappings},
author = {Arbeláez and H. and Hernández and R. and Sierra W},
journal= {arXiv preprint arXiv:2107.01756},
year = {2021}
}