A spinor proof of the classification of stable minimal surfaces in $\mathbb{R}^3$

TL;DR

This paper provides a new proof that all complete, two-sided, stable minimal surfaces in three-dimensional space are flat, utilizing index theory for Dirac operators on twisted spinor bundles.

Contribution

It introduces a spinor-based proof for the classification of stable minimal surfaces, offering a novel approach compared to traditional methods.

Findings

All complete two-sided stable minimal surfaces in R^3 are flat.

The proof employs index theory for Dirac operators on twisted spinor bundles.

The approach simplifies understanding of the classification theorem.

Abstract

We give a proof that every complete two-sided stable minimal surface in $\mathbb{R}^3$ is flat using the index theory for Dirac operators on twisted spinor bundles.