Minimizers of the Willmore functional under fixed conformal class

Details Minimizers of the Willmore functional under fixed conformal class Minimizers of the Willmore functional under fixed conformal class

2010-09-30

arxiv.org/abs/1009.6168v1

Mathematics

Differential Geometry

Scientific paper

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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