Superposition of Harmonic Surfaces: Helical Motifs in Lamellar Structures

Abstract: We study harmonic surfaces in $\mathbb{R}^3$ through the framework of harmonic Enneper immersions and prove a superposition principle for such surfaces. We prove that minimal and maximal surfaces admit a decomposition into harmonic components. Applications include the construction of finite and infinite configurations of helical motifs, an asymptotic analysis via multipole expansions, and the modelling of twist grain boundary phases in lamellar systems.