Hypersurfaces with Null Higher Order Anisotropic Mean Curvature
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-24
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
Given a positive function F on ?n which satisfies a convexity condition, for 1≤r≤n, we define for hypersurfaces in ℝn+1 the rth anisotropic mean curvature function Hr;F, a generalization of the usual rth mean curvature function.
We call a hypersurface anisotropic minimal if HF=H1;F=0, and anisotropic r-minimal if Hr+1;F=0.
Let W be the set of points which are omitted by the hyperplanes tangent to M.
We will prove that if an oriented hypersurface M is anisotropic minimal, and the set W is open and nonempty, then x(M) is a part of a hyperplane of ℝn+1.
We also prove that if an oriented hypersurface M is anisotropic r-minimal and its rth anisotropic mean curvature Hr;F is nonzero everywhere, and the set W is open and nonempty, then M has anisotropic relative nullity n−r.
American Psychological Association (APA)
Wang, Hua& He, Yijun. 2013. Hypersurfaces with Null Higher Order Anisotropic Mean Curvature. Geometry،Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-493051
Modern Language Association (MLA)
Wang, Hua& He, Yijun. Hypersurfaces with Null Higher Order Anisotropic Mean Curvature. Geometry No. 2013 (2013), pp.1-7.
https://search.emarefa.net/detail/BIM-493051
American Medical Association (AMA)
Wang, Hua& He, Yijun. Hypersurfaces with Null Higher Order Anisotropic Mean Curvature. Geometry. 2013. Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-493051
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-493051