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Lifespan theorem and gap lemma for the globally constrained Willmore flow

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


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