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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| Format: | Article |
| Language: | English |
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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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| author | Yanqi Zhu Jin Liu Guohua Wu |
| author_facet | Yanqi Zhu Jin Liu Guohua Wu |
| author_sort | Yanqi Zhu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-14ea4790adfb45449c8e8eac0222e39a |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-14ea4790adfb45449c8e8eac0222e39a2025-02-03T01:11:48ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/697132697132Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit SphereYanqi Zhu0Jin Liu1Guohua Wu2College of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, ChinaCollege of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, ChinaCollege of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, ChinaFor 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.http://dx.doi.org/10.1155/2014/697132 |
| spellingShingle | Yanqi Zhu Jin Liu Guohua Wu Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere The Scientific World Journal |
| title | Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere |
| title_full | Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere |
| title_fullStr | Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere |
| title_full_unstemmed | Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere |
| title_short | Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere |
| title_sort | gap phenomenon of an abstract willmore type functional of hypersurface in unit sphere |
| url | http://dx.doi.org/10.1155/2014/697132 |
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