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Asymptotic estimates for the Willmore flow with small energy

Scheuer, Julian and Kuwert, Ernst 2020. Asymptotic estimates for the Willmore flow with small energy. International Mathematics Research Notices 10.1093/imrn/rnaa015

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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.

Item Type: Article
Date Type: Published Online
Status: In Press
Schools: Mathematics
Publisher: Oxford University Press
ISSN: 1073-7928
Date of First Compliant Deposit: 21 April 2020
Date of Acceptance: 17 January 2020
Last Modified: 01 Mar 2021 03:05

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