TITLE:
Properties of Harmonic Functions on Koch Curve
AUTHORS:
Guangjun Yang, Ping Wang
KEYWORDS:
Koch Curve, Harmonic Functions, Quaternary Derivatives
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.2,
February
5,
2026
ABSTRACT: Recently, we discussed the properties of harmonic functions on the Sierpinski gasket (SG) and proved the Holder derivative of the harmonic functions. In this paper, based on the quaternary expressions of the Koch curve, another very important fractal, we will construct harmonic functions on the fractal and discuss some properties of the derivative of the harmonic functions. The main result is that first quaternary derivative is found to be constant.