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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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  • [1]

    G. Huisken, The volume preserving mean curvature flow, J. Reine Angew. Math., 382 (1987), 35-48.doi: 10.1515/crll.1987.382.35.

    [2]

    H. Y. Jian and Y. N. Liu, Long-time existence of mean curvature flow with external force fields, Pacific J. Math., 234 (2008), 311-324.doi: 10.2140/pjm.2008.234.311.

    [3]

    E. Kuwert and R. Schätzle, The Willmore flow with small initial energy, J. Differential Geom., 57 (2001), 409-441.

    [4]

    E. Kuwert and R. Schätzle, Gradient flow for the Willmore functional, Comm. Anal. Geom., 10 (2002), 307-339.

    [5]

    Y. N. Liu, Gradient flow for the Helfrich functional, Chin. Ann. Math. B, 33 (2012), 931-940.doi: 10.1007/s11401-012-0741-0.

    [6]

    J. McCoy, The surface area preserving mean curvature flow, Asian J. Math., 7 (2003), 7-30.

    [7]

    J. McCoy and G. WheelerFinite time singularities for the locally constrained willmore flow of surfaces, preprint, arXiv:1201.4541.

    [8]

    J.McCoy, G. Wheeler and G. Williams, Lifespan theorem for constrained surface diffusion flows, Math. Z., 269 (2011), 147-178.doi: 10.1007/s00209-010-0720-7.

    [9]

    G. Simonett, The Willmore flow near spheres, Differential Integral Equations, 14 (2001), 1005-1014.

    [10]

    G. Wheeler, "Fourth Order Geometric Evolution Equations," Ph.D thesis, University of Wollongong, 2010.doi: 10.1017/s0004972710001863.

    [11]

    G. Wheeler, Lifespan Theorem for simple constrained surface diffusion flows, J. Math. Anal. Appl., 375 (2011), 685-698.doi: 10.1016/j.jmaa.2010.09.043.

    [12]

    T. Willmore, "Riemannian Geometry," Oxford University Press, New York, 1993.doi: 10.2307/3612154.

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