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Minimizers of the willmore functional under fixed conformal class

Ernst Kuwert Albert-Ludwigs-Universit¨at Freiburg Reiner Sch¨atzle Eberhard-Karls-Universit¨at T¨ubingen

Differential Geometry mathscidoc:1609.10306

Journal of Differential Geometry, 93, (3), 471-530, 2013
We prove the existence of a smooth minimizer of the Willmore energy in the class of conformal immersions of a given closed Riemann surface into IRn, n = 3, 4, if there is one conformal immersion with Willmore energy smaller than a certain bound Wn,p depending on codimension and genus p of the Riemann surface. For tori in codimension 1, we know W3,1 = 8 .
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@inproceedings{ernst2013minimizers,
  title={MINIMIZERS OF THE WILLMORE FUNCTIONAL UNDER FIXED CONFORMAL CLASS},
  author={Ernst Kuwert, and Reiner Sch¨atzle},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914074644139726968},
  booktitle={Journal of Differential Geometry},
  volume={93},
  number={3},
  pages={471-530},
  year={2013},
}
Ernst Kuwert, and Reiner Sch¨atzle. MINIMIZERS OF THE WILLMORE FUNCTIONAL UNDER FIXED CONFORMAL CLASS. 2013. Vol. 93. In Journal of Differential Geometry. pp.471-530. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914074644139726968.
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