The spinorial energy functional on surfaces

TL;DR

This paper investigates the properties of the spinorial energy functional on surfaces, highlighting its scale invariance, critical points, and connection to the Willmore energy through the spinorial Weierstra{\

Contribution

It extends the study of the spinorial energy functional to surfaces, revealing its critical points and relation to classical surface energies.

Findings

The functional is scale-invariant on surfaces.

Critical points are abundant due to scale invariance.

Connections to Willmore energy via spinorial Weierstra{\

Abstract

This is a companion paper to arXiv:1207.3529 where we introduced the spinorial energy functional and studied its main properties in dimensions equal or greater than three. In this article we focus on the surface case. A salient feature here is the scale invariance of the functional which leads to a plenitude of critical points. Moreover, via the spinorial Weierstra{\ss} representation it relates to the Willmore energy of periodic immersions of surfaces into $\mathbb{R}^3$.