Asymptotic Estimates for the Willmore Flow With Small Energy

Kuwert and Schatzle 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 Muller (2006) and an estimate for the isoperimetric deficit by Roger and Schatzle (2012), whose original proofs used different methods.