Linear Superposition of Minimal Surfaces: Generalized Helicoids and Minimal Cones

TL;DR

This paper introduces a linear superposition principle for minimal hypersurfaces, leading to the discovery of new algebraic minimal cones and generalized helicoids with high degrees in Euclidean space.

Contribution

It presents a novel superposition approach that generates new minimal hypersurfaces and cones, expanding the known classes of minimal surfaces in Euclidean space.

Findings

New minimal hypersurfaces constructed via superposition.

Linear combinations of generalized helicoids produce high-degree minimal cones.

The approach broadens the understanding of minimal surface families.

Abstract

Observing a linear superposition principle, a family of new minimal hypersurfaces in Euclidean space is found, as well as that linear combinations of generalized helicoids induce new algebraic minimal cones of arbitrarily high degree.