Mathematische Zeitschrift

, Volume 282, Issue 1–2, pp 177–202 | Cite as

The spinorial energy functional on surfaces

  • Bernd Ammann
  • Hartmut Weiss
  • Frederik Witt


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 \(\mathbb {R}^3\).



The authors thank T. Friedrich for providing interesting references and the referee for carefully reading the manuscript.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  2. 2.Mathematisches Seminar der Universität KielKielGermany
  3. 3.Institut für Geometrie und Topologie der Universität StuttgartStuttgartGermany

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