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Stable closed equilibria for anisotropic surface energies: Surfaces with edges
1. | Department of Mathematics, Idaho State University, Pocatello , Idaho, 83209, United States |
References:
[1] |
J. L. Barbosa and M. do Carmo, Stability of hypersurfaces with constant mean curvature, Math. Z., 185 (1984), 339-353.
doi: 10.1007/BF01215045. |
[2] |
J. E. Brothers and F. Morgan, The isoperimetric theorem for general integrands, Michigan Math. J., 41 (1994), 419-431.
doi: 10.1307/mmj/1029005070. |
[3] |
J. W. Cahn and D. W. Hoffman, A vector thermodynamics for anisotropic surfaces. II. Curved and faceted surfaces, Acta Metallurgica, 22 (1974), 1205-1214.
doi: 10.1016/0001-6160(74)90134-5. |
[4] |
Y. Giga, "Surface Evolution Equations. A Level Set Approach," Monographs in Mathematics, 99, Birkhäuser Verlag, Basel, 2006. |
[5] |
Y. He, H. Li, H. Ma and J. Ge, Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures, Indiana Univ. Math. J., 58 (2009), 853-868.
doi: 10.1512/iumj.2009.58.3515. |
[6] |
Y. He and H. Li, A new variational characterization of the Wulff shape, Differential Geom. Appl., 26 (2008), 377-390. |
[7] |
Y. He and H. Li, Stability of hypersurfaces with constant (r+1)-th anisotropic mean curvature, Illinois J. Math., 52 (2008), 1301-1314. |
[8] |
M. Koiso and B. Palmer, Geometry and stability of surfaces with constant anisotropic mean curvature, Indiana Univ. Math. J., 54 (2005), 1817-1852.
doi: 10.1512/iumj.2005.54.2613. |
[9] |
M. Koiso and B. Palmer, Stability of anisotropic capillary surfaces between two parallel planes, Calculus of Variations and Partial Differential Equations, 25 (2006), 275-298. |
[10] |
M. Koiso and B. Palmer, Rolling construction for anisotropic Delaunay surfaces, Pacific J. Math., 234 (2008), 345-378. |
[11] |
M. Koiso and B. Palmer, Anisotropic umbilic points and Hopf's theorem for constant anisotropic mean curvature, Indiana Univ. Math. J., 59 (2010), 79-90.
doi: 10.1512/iumj.2010.59.4164. |
[12] |
F. Morgan, Planar Wulff shape is unique equilibrium, Proc. Amer. Math. Soc., 133 (2005), 809-813.
doi: 10.1090/S0002-9939-04-07661-0. |
[13] |
B. Palmer, Stability of the Wulff shape, Proc. Amer. Math. Soc., 126 (1998), 3661-3667.
doi: 10.1090/S0002-9939-98-04641-3. |
[14] |
H. C. Wente, A note on the stability theorem of J. L. Barbosa and M. Do Carmo for closed surfaces of constant mean curvature, Pacific J. Math., 147 (1991), 375-379. |
[15] |
S. Winklmann, A note on the stability of the Wulff shape, Arch. Math. (Basel), 87 (2006), 272-279.
doi: 10.1007/s00013-006-1685-y. |
show all references
References:
[1] |
J. L. Barbosa and M. do Carmo, Stability of hypersurfaces with constant mean curvature, Math. Z., 185 (1984), 339-353.
doi: 10.1007/BF01215045. |
[2] |
J. E. Brothers and F. Morgan, The isoperimetric theorem for general integrands, Michigan Math. J., 41 (1994), 419-431.
doi: 10.1307/mmj/1029005070. |
[3] |
J. W. Cahn and D. W. Hoffman, A vector thermodynamics for anisotropic surfaces. II. Curved and faceted surfaces, Acta Metallurgica, 22 (1974), 1205-1214.
doi: 10.1016/0001-6160(74)90134-5. |
[4] |
Y. Giga, "Surface Evolution Equations. A Level Set Approach," Monographs in Mathematics, 99, Birkhäuser Verlag, Basel, 2006. |
[5] |
Y. He, H. Li, H. Ma and J. Ge, Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures, Indiana Univ. Math. J., 58 (2009), 853-868.
doi: 10.1512/iumj.2009.58.3515. |
[6] |
Y. He and H. Li, A new variational characterization of the Wulff shape, Differential Geom. Appl., 26 (2008), 377-390. |
[7] |
Y. He and H. Li, Stability of hypersurfaces with constant (r+1)-th anisotropic mean curvature, Illinois J. Math., 52 (2008), 1301-1314. |
[8] |
M. Koiso and B. Palmer, Geometry and stability of surfaces with constant anisotropic mean curvature, Indiana Univ. Math. J., 54 (2005), 1817-1852.
doi: 10.1512/iumj.2005.54.2613. |
[9] |
M. Koiso and B. Palmer, Stability of anisotropic capillary surfaces between two parallel planes, Calculus of Variations and Partial Differential Equations, 25 (2006), 275-298. |
[10] |
M. Koiso and B. Palmer, Rolling construction for anisotropic Delaunay surfaces, Pacific J. Math., 234 (2008), 345-378. |
[11] |
M. Koiso and B. Palmer, Anisotropic umbilic points and Hopf's theorem for constant anisotropic mean curvature, Indiana Univ. Math. J., 59 (2010), 79-90.
doi: 10.1512/iumj.2010.59.4164. |
[12] |
F. Morgan, Planar Wulff shape is unique equilibrium, Proc. Amer. Math. Soc., 133 (2005), 809-813.
doi: 10.1090/S0002-9939-04-07661-0. |
[13] |
B. Palmer, Stability of the Wulff shape, Proc. Amer. Math. Soc., 126 (1998), 3661-3667.
doi: 10.1090/S0002-9939-98-04641-3. |
[14] |
H. C. Wente, A note on the stability theorem of J. L. Barbosa and M. Do Carmo for closed surfaces of constant mean curvature, Pacific J. Math., 147 (1991), 375-379. |
[15] |
S. Winklmann, A note on the stability of the Wulff shape, Arch. Math. (Basel), 87 (2006), 272-279.
doi: 10.1007/s00013-006-1685-y. |
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