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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/697132 |
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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. |
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| ISSN: | 2356-6140 1537-744X |