Triply periodic minimal surfaces which converge to the Hoffman-Wohlgemuth example

TL;DR

This paper introduces a new continuous family of embedded minimal surfaces with two-dimensional period problems, demonstrating convergence to known examples like the Scherk second surface and Hoffman-Wohlgemuth example.

Contribution

It constructs a novel one-parameter family of minimal surfaces and establishes their limits to classical examples, advancing understanding of minimal surface moduli.

Findings

New family of embedded minimal surfaces with two-dimensional period problems

Convergence to Scherk second surface and Hoffman-Wohlgemuth example

Enhanced understanding of minimal surface limits and classifications

Abstract

We get a continuous one-parameter new family of embedded minimal surfaces, of which the period problems are two-dimensional. Moreover, one proves that it has Scherk second surface and Hoffman-Wohlgemuth example as limit-members.