Complex and Quaternionic Cauchy formulas in Koch snowflakes
Marisel Avila Alfaro, Ricardo Abreu Blaya
TL;DR
This paper develops Cauchy integral formulas for holomorphic and hyperholomorphic functions within domains bounded by Koch snowflakes in 2D and 3D, extending complex analysis to fractal boundaries.
Contribution
It introduces new Cauchy formulas applicable to fractal boundaries like Koch snowflakes in both two and three dimensions.
Findings
Derived Cauchy integral formulas for Koch snowflake boundaries.
Extended complex and hyperholomorphic function theory to fractal domains.
Provided mathematical tools for analysis on fractal geometries.
Abstract
In this paper we derive a Cauchy integral formula for holomorphic and hyperholomorphic functions in domains bounded by a Koch snowflake in two and three dimensional setting.
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