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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Official URL: http://dx.doi.org/10.1093/imrn/rnaa015
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.
Item Type: | Article |
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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: | 07 Dec 2020 16:56 |
URI: | http://orca.cf.ac.uk/id/eprint/131158 |
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