English

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 D\mathbb{D}. 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.

Keywords

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}
}
R2 v1 2026-06-24T03:53:04.381Z