English

Minimizers of the Willmore functional under fixed conformal class

Differential Geometry 2010-10-01 v1

Abstract

We consider the problem of minimizing the Willmore energy in the class of conformal immersions of a given closed, genus p Riemann surface into R^n for n=3,4. We prove existence of a smooth minimizer, provided that the infimum is below a certain bound W(n,p){\cal W}(n,p). For tori in R^3 we have explicitely W(3,1)=8π{\cal W}(3,1) = 8\pi.

Keywords

Cite

@article{arxiv.1009.6168,
  title  = {Minimizers of the Willmore functional under fixed conformal class},
  author = {Ernst Kuwert and Reiner Schätzle},
  journal= {arXiv preprint arXiv:1009.6168},
  year   = {2010}
}
R2 v1 2026-06-21T16:21:43.741Z