Willmore Surfaces of Revolution with Two Prescribed Boundary Circles

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• 作者：Matthias Bergner (1)
  Anna Dall’Acqua (2)
  Steffen Fr?hlich (3)
  
• 关键词：Natural boundary conditions ; Willmore surface ; Surface of revolution ; 49Q10 ; 53C42 ; 35J65 ; 34L30
• 刊名：Journal of Geometric Analysis
• 出版年：2013
• 出版时间：January 2013
• 年：2013
• 卷：23
• 期：1
• 页码：283-302
• 全文大小：376KB
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• 作者单位：Matthias Bergner (1)
  Anna Dall’Acqua (2)
  Steffen Fr?hlich (3)
  
  1. Institut für Differentialgeometrie, Gottfried Wilhelm Leibniz Universit?t Hannover, Welfengarten 1, 30167, Hannover, Germany
  2. Fakult?t für Mathematik, Otto-von-Guericke-Universit?t, Universit?tsplatz 2, 39016, Magdeburg, Germany
  3. FB08 Institut für Mathematik, Johannes Gutenberg-Universit?t Mainz, Staudingerweg 9, 55099, Mainz, Germany
  
• ISSN：1559-002X

文摘

We consider the family of smooth embedded surfaces of revolution in??sup class="a-plus-plus">3 having two concentric circles contained in two parallel planes of ?sup class="a-plus-plus">3 as boundary. Minimizing the Willmore functional within this class of surfaces we prove the existence of smooth axi-symmetric Willmore surfaces having these circles as boundary. When the radii of the circles tend to zero we prove convergence of these solutions to the round sphere.