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Formal equivalence between normal forms of reversible and hamiltonian dynamical systems
Lifespan theorem and gap lemma for the globally constrained Willmore flow
1. | Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China |
2. | College of Mathematics and Information Science, Henan Normal University, Henan, 453007 |
References:
[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. Wheeler, Finite 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. |
show all references
References:
[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. Wheeler, Finite 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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