Lifespan theorem and gap lemma for the globally constrained Willmore flow

Yannan Liu; Linfen Cao

doi:10.3934/cpaa.2014.13.715

Article Contents

2014, Volume 13, Issue 2: 715-728. Doi: 10.3934/cpaa.2014.13.715

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Lifespan theorem and gap lemma for the globally constrained Willmore flow

Yannan Liu^1, and
Linfen Cao^2,

1.
Department of Mathematics, Beijing Technology and Business University, Beijing 100048
2.
College of Mathematics and Information Science, Henan Normal University, Henan, 453007

Received: February 28, 2013

Revised: June 30, 2013

Published: February 2014

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Abstract

We study a fourth-order flow, which can be seen as a globally constrained Willmore flow. We obtain a lower bound on the lifespan of the smooth solution, which depends on the concentration of curvature for the initial surface and the constrained term. We also give a gap lemma for this flow, which is an important lemma in the study of the blowup analysis.

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Mathematics Subject Classification: Primary: 35J60, 35K45, 52K44,53A05.

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References

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