Hypersurfaces with Null Higher Order Anisotropic Mean Curvature
Keyword(s):
Given a positive function on which satisfies a convexity condition, for , we define for hypersurfaces in the th anisotropic mean curvature function , a generalization of the usual th mean curvature function. We call a hypersurface anisotropic minimal if , and anisotropic -minimal if . Let be the set of points which are omitted by the hyperplanes tangent to . We will prove that if an oriented hypersurface is anisotropic minimal, and the set is open and nonempty, then is a part of a hyperplane of . We also prove that if an oriented hypersurface is anisotropic -minimal and its th anisotropic mean curvature is nonzero everywhere, and the set is open and nonempty, then has anisotropic relative nullity .
2017 ◽
Vol 446
(1)
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pp. 1046-1059
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Keyword(s):
2013 ◽
Vol 31
(2)
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pp. 175-189
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Keyword(s):
2010 ◽
Vol 59
(1)
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pp. 79-90
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Keyword(s):
2007 ◽
Vol 143
(3)
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pp. 703-729
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