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math.DG2010
Minimizers of the Willmore functional under fixed conformal class
Ernst Kuwert, Reiner Schätzle
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…
math.DG2010
Closed surfaces with bounds on their Willmore energy
Ernst Kuwert, Reiner Schätzle
The Willmore energy of a closed surface in R^n is the integral of its squared mean curvature, and is invariant uner Möbius transformations of R^n. We show that any torus in R^3 wit…