Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere

For an n-dimensional hypersurface in unit sphere, we introduce an abstract Willmore type called Wn,F-Willmore functional, which generalizes the well-known classic Willmore functional. Its critical point is called the Wn,F-Willmore hypersurface, for which the variational equation and Simons’ type int...

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Bibliographic Details
Published in:TheScientificWorld 2014-01, Vol.2014 (2014), p.1-8
Main Authors: Zhu, Yanqi, Wu, Guohua, Liu, Jin
Format: Article
Language:English
Subjects:
Equality
Mathematical Concepts
Mathematical research
Power plants
Sphere
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Summary:For an n-dimensional hypersurface in unit sphere, we introduce an abstract Willmore type called Wn,F-Willmore functional, which generalizes the well-known classic Willmore functional. Its critical point is called the Wn,F-Willmore hypersurface, for which the variational equation and Simons’ type integral equalities are obtained. Moreover, we construct a few examples of Wn,F-Willmore hypersurface and give a gap phenomenon characterization by use of our integral formula.
ISSN:2356-6140
1537-744X
1537-744X
DOI:10.1155/2014/697132