A note on special polynomials and minimal surfaces

TL;DR

This paper explores the connection between special polynomials satisfying hypergeometric equations and the construction of minimal surfaces, providing explicit examples of such surfaces.

Contribution

It demonstrates how roots of hypergeometric polynomials can be used to construct minimal surfaces, extending Traizet's regeneration technique with concrete examples.

Findings

Examples of minimal surfaces linked to hypergeometric polynomial roots

Explicit constructions illustrating the theoretical framework

Insights into the algebraic structure of minimal surfaces

Abstract

When using Traizet's regeneration technique to construct minimal surfaces, the simplest nontrivial configurations are given as the roots of polynomials that satisfy a hypergeometric differential equation. We exhibit examples of simple minimal surfaces exhibiting the same behavior.