How We Found the Test Function for Branched Stable Minimal Immersions
An AI-Assisted Computational Research Note
Abstract. This note describes how we found a test function used in our study of branched stable minimal immersions. Starting from a capillary prototype, we combined hand calculations with AI-assisted programming, principally through GitHub Copilot and Cursor's Composer 2, to generate and test numerical experiments rapidly. These tools were used mainly for coding rather than mathematical reasoning. We expect increasingly capable AI tools to accelerate mathematical exploration and deepen, rather than replace, human understanding.
Capillary prototype
Balanced $2/m$ tail
Small-$k$ limit
Linear zero model
Cutoff ODE
Contents
Gaoming Wang
Assistant Professor
My research interests include Geometric Analysis and Partial Differential Equations.