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Willmore Surfaces of Revolution with Two Prescribed Boundary Circles

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Abstract

We consider the family of smooth embedded surfaces of revolution in ℝ3 having two concentric circles contained in two parallel planes of ℝ3 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.

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Authors and Affiliations

  1. Institut für Differentialgeometrie, Gottfried Wilhelm Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Matthias Bergner

  2. Fakultät für Mathematik, Otto-von-Guericke-Universität, Universitätsplatz 2, 39016, Magdeburg, Germany

    Anna Dall’Acqua

  3. FB08 Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55099, Mainz, Germany

    Steffen Fröhlich

Authors
  1. Matthias Bergner
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  2. Anna Dall’Acqua
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  3. Steffen Fröhlich
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Correspondence to Matthias Bergner.

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Bergner, M., Dall’Acqua, A. & Fröhlich, S. Willmore Surfaces of Revolution with Two Prescribed Boundary Circles. J Geom Anal 23, 283–302 (2013). https://doi.org/10.1007/s12220-011-9248-2

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  • DOI: https://doi.org/10.1007/s12220-011-9248-2

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