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Kuwert and Sch\"atzle showed in 2001 that the Willmore flow converges to astandard round sphere, if the initial energy is small. In this situation, weprove stability estimates for the barycenter and the quadratic moment of thesurface. Moreover, in codimension one we obtain stability bounds for theenclosed volume and averaged mean curvature. As direct applications, we recovera quasi-rigidity estimate due to De Lellis and M\"uller (2006) and an estimatefor the isoperimetric deficit by R\"oger and Sch\"atzle (2012), whose originalproofs used different methods.

Asymptotic estimates for the Willmore flow with small energy