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arXiv · 1009.6168

Minimizers of the Willmore functional under fixed conformal class

Ernst Kuwert·Reiner Schätzle
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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 ${\cal W}(n,p)$. For tori in R^3 we have explicitely ${\cal W}(3,1) = 8\pi$.

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Ernst Kuwert, Reiner Schätzle. 2010-09-30. Minimizers of the Willmore functional under fixed conformal class. https://arxiv.org/abs/1009.6168

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