Zusammenfassung

This is a companion paper to [1] where we introduced the spino-
rial 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 Weierstraß representation it relates
to the Willmore energy of periodic immersions of surfaces into R3.