Abstract
This is a companion paper to (Ammann et al. in A spinorial energy functional: critical points and gradient flow. arXiv:1207.3529, 2012) 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 Weierstraß representation it relates to the Willmore energy of periodic immersions of surfaces into \(\mathbb {R}^3\).
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The authors thank T. Friedrich for providing interesting references and the referee for carefully reading the manuscript.
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Ammann, B., Weiss, H. & Witt, F. The spinorial energy functional on surfaces. Math. Z. 282, 177–202 (2016). https://doi.org/10.1007/s00209-015-1537-1
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DOI: https://doi.org/10.1007/s00209-015-1537-1