The spinorial energy functional on surfaces

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• 作者：Bernd Ammann ; Hartmut Weiss ; Frederik Witt
• 刊名：Mathematische Zeitschrift
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：282
• 期：1-2
• 页码：177-202
• 全文大小：619 KB
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• 作者单位：Bernd Ammann (1)
  Hartmut Weiss (2)
  Frederik Witt (3)
  
  1. Fakultät für Mathematik, Universität Regensburg, Universitätsstrasse 40, 93040, Regensburg, Germany
  2. Mathematisches Seminar der Universität Kiel, Ludewig-Meyn Strasse 4, 24098, Kiel, Germany
  3. Institut für Geometrie und Topologie der Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1823

文摘

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