A limit-method for solving period problems on minimal surfaces

TL;DR

The paper presents a new limit-method technique for solving period problems in minimal surfaces, leveraging convergence of Weierstrass data to known examples to identify closed periods.

Contribution

It introduces a novel limit-method approach that uses convergence properties of Weierstrass data to solve period problems in minimal surfaces.

Findings

The limit-method successfully finds sub-families with closed periods.

It provides a new tool for analyzing minimal surface families.

The technique applies to known examples and converging data.

Abstract

We introduce a new technique to solve period problems on minimal surfaces called limit-method. If a family of surfaces has Weierstrass-data converging to the data of a known example, and this presents a transversal solution of periods, then the original family contains a sub-family with closed periods.