@article{Liang2025, 
author = {Xiaotong Liang and Chunxue Duan and Zihan Su and Yonghong Xie},
title = {k-monogenic functions and Möbius transformations},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {29132-29150},
keywords = {Möbius transformation, k-monogenic function, Schwarz-Pick-type lemma},
url = {https://www.sciopen.com/article/10.3934/math.20251281},
doi = {10.3934/math.20251281},
abstract = {Clifford analysis is a fundamental framework for extending complex function theory to high-dimensional spaces, where    k-monogenic functions (high-order generalizations of monogenic functions) play a pivotal role in geometric function theory and partial differential equations. However, there is a paucity of research findings regarding the Möbius transformations of    k-monogenic functions for arbitrary    k. In this paper, we first derived that the composite function constructed from a    k-monogenic function and a Möbius transformation remains    k-monogenic when    k  =  2  ,    3  ,    4, and was generalized to the general case. Then, as applications, we proved the Schwarz-Pick-type lemma for harmonic functions using a new method, and we gave a version of the Schwarz-Pick-type lemma for inframonogenic functions. This work fills the gap in the transformation theory of    k-monogenic functions, enriches the family of Schwarz-Pick-type lemmas in Clifford analysis, and provides theoretical tools to solve research related to high-dimensional geometric function theory.}
}