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Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow
A nonlinear partial differential equation for the volume preserving mean curvature flow
1. | Department of Applied Mathematics, University of Crete, 714 09 Heraklion |
References:
[1] |
N. D. Alikakos and A. Freire, The normalized mean curvature flow for a small bubble in a Riemannian manifold, J. Differential Geom., 64 (2003), 247-303. |
[2] |
D. C. Antonopoulou, G. D. Karali and I. M. Sigal, Stability of spheres under volume preserving mean curvature flow, Dynamics of PDE, 7 (2010), 327-344. |
[3] |
J. Escher and G. Simonett, A center manifold analysis for the mullins-sekerka model, J. Differential Eq., 143 (1998), 267-292.
doi: 10.1006/jdeq.1997.3373. |
[4] |
J. Escher and G. Simonett, The volume preserving mean curvature flow near spheres, Proc. Amer. Math. Soc., 126 (1998), 2789-2796.
doi: 10.1090/S0002-9939-98-04727-3. |
[5] |
M. Gage, On an area-preserving evolution equation for plane curves, Nonlinear Problems in Geometry, D. M. DeTurck, editor, Contemp. Math., 51 (1986), AMS, Providence, 51-62.
doi: 10.1090/conm/051/848933. |
[6] |
M. Gage and R. Hamilton, The Heat equation shrinking convex plane curves, J. Differential Geom., 23 (1986), 69-96. |
[7] |
Z. Gang and I. M. Sigal, Neck pinching dynamics under mean curvature flow, J. Geom. Anal., 19 (2009), 36-80.
doi: 10.1007/s12220-008-9050-y. |
[8] |
M. A. Grayson, The Heat Equation shrinks embedded plane curves to round points, J. Differential Geom., 26 (1987), 285-314. |
[9] |
G. Huisken, The volume preserving mean curvature flow, J. Reine Angew. Math., 382 (1987), 35-48.
doi: 10.1515/crll.1987.382.35. |
[10] |
E. Kreyszig, "Differential Geometry," Dover Publications, New York, 1991. |
[11] |
N. Shimakura, "Partial Differential Operators of Elliptic Type," Translations of Mathematical Monographs, 99, 1992. |
[12] |
M. Struwe, Geometric evolution problems. Nonlinear partial differential equations in differential geometry, IAS/Park City Math. Ser., 2, Amer. Math. Soc., Providence, RI, Park City, UT, (1992), 257-339. |
show all references
References:
[1] |
N. D. Alikakos and A. Freire, The normalized mean curvature flow for a small bubble in a Riemannian manifold, J. Differential Geom., 64 (2003), 247-303. |
[2] |
D. C. Antonopoulou, G. D. Karali and I. M. Sigal, Stability of spheres under volume preserving mean curvature flow, Dynamics of PDE, 7 (2010), 327-344. |
[3] |
J. Escher and G. Simonett, A center manifold analysis for the mullins-sekerka model, J. Differential Eq., 143 (1998), 267-292.
doi: 10.1006/jdeq.1997.3373. |
[4] |
J. Escher and G. Simonett, The volume preserving mean curvature flow near spheres, Proc. Amer. Math. Soc., 126 (1998), 2789-2796.
doi: 10.1090/S0002-9939-98-04727-3. |
[5] |
M. Gage, On an area-preserving evolution equation for plane curves, Nonlinear Problems in Geometry, D. M. DeTurck, editor, Contemp. Math., 51 (1986), AMS, Providence, 51-62.
doi: 10.1090/conm/051/848933. |
[6] |
M. Gage and R. Hamilton, The Heat equation shrinking convex plane curves, J. Differential Geom., 23 (1986), 69-96. |
[7] |
Z. Gang and I. M. Sigal, Neck pinching dynamics under mean curvature flow, J. Geom. Anal., 19 (2009), 36-80.
doi: 10.1007/s12220-008-9050-y. |
[8] |
M. A. Grayson, The Heat Equation shrinks embedded plane curves to round points, J. Differential Geom., 26 (1987), 285-314. |
[9] |
G. Huisken, The volume preserving mean curvature flow, J. Reine Angew. Math., 382 (1987), 35-48.
doi: 10.1515/crll.1987.382.35. |
[10] |
E. Kreyszig, "Differential Geometry," Dover Publications, New York, 1991. |
[11] |
N. Shimakura, "Partial Differential Operators of Elliptic Type," Translations of Mathematical Monographs, 99, 1992. |
[12] |
M. Struwe, Geometric evolution problems. Nonlinear partial differential equations in differential geometry, IAS/Park City Math. Ser., 2, Amer. Math. Soc., Providence, RI, Park City, UT, (1992), 257-339. |
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