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math.DG2011
Control of the isoperimetric deficit by the Willmore deficit
Matthias Röger, Reiner Schätzle
In the class of smoothly embedded surfaces of sphere type we prove that the isoperimetric deficit can be controlled by the Willmore deficit.
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…