Year: 2025
Type: article
Abstract: Recently, it is proven that positive harmonic functions defined in the unit disc or the upper half-plane in $\mathbb{C}$ are contractions in hyperbolic metrics [14]. Furthermore, the same result does not hold in higher dimensions as shown by given counterexamples [16]. In this paper, we shall show that positive (or bounded) harmonic functions defined in the unit ball in $\mathbb{R}^{n}$ are Lipschitz in hyperbolic metrics. The involved method in main results allows to establish essential improvements of Schwarz type inequalities for monogenic functions in Clifford analysis [24, 25] and octonionic analysis [21] in a unified approach.
Authors: Zhenghua Xu, Ting Yu, Qinghai Huo
Institution: Hefei University of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407092556