Abstract
Abstract Kuwert and Schätzle showed in 2001 that the Willmore flow converges to a standard round sphere, if the initial energy is small. In this situation, we prove stability estimates for the barycenter and the quadratic moment of the surface. Moreover, in codimension one, we obtain stability bounds for the enclosed volume and averaged mean curvature. As direct applications, we recover a quasi-rigidity estimate due to De Lellis and Müller (2006) and an estimate for the isoperimetric deficit by Röger and Schätzle (2012), whose original proofs used different methods.
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