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 W ((n,F))-Willmore functional, which generalizes the well-known classic Willmore functional. Its critical point is called the W ((n,F))-Willmore hypersurface, for which the variational equation and Simons...

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Detalles Bibliográficos
Autores principales: Zhu, Yanqi, Liu, Jin, Wu, Guohua
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4070580/
https://www.ncbi.nlm.nih.gov/pubmed/25003147
http://dx.doi.org/10.1155/2014/697132
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author Zhu, Yanqi
Liu, Jin
Wu, Guohua
author_facet Zhu, Yanqi
Liu, Jin
Wu, Guohua
author_sort Zhu, Yanqi
collection PubMed
description For an n-dimensional hypersurface in unit sphere, we introduce an abstract Willmore type called W ((n,F))-Willmore functional, which generalizes the well-known classic Willmore functional. Its critical point is called the W ((n,F))-Willmore hypersurface, for which the variational equation and Simons' type integral equalities are obtained. Moreover, we construct a few examples of W ((n,F))-Willmore hypersurface and give a gap phenomenon characterization by use of our integral formula.
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spelling pubmed-40705802014-07-07 Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere Zhu, Yanqi Liu, Jin Wu, Guohua ScientificWorldJournal Research Article For an n-dimensional hypersurface in unit sphere, we introduce an abstract Willmore type called W ((n,F))-Willmore functional, which generalizes the well-known classic Willmore functional. Its critical point is called the W ((n,F))-Willmore hypersurface, for which the variational equation and Simons' type integral equalities are obtained. Moreover, we construct a few examples of W ((n,F))-Willmore hypersurface and give a gap phenomenon characterization by use of our integral formula. Hindawi Publishing Corporation 2014 2014-06-05 /pmc/articles/PMC4070580/ /pubmed/25003147 http://dx.doi.org/10.1155/2014/697132 Text en Copyright © 2014 Yanqi Zhu et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Zhu, Yanqi
Liu, Jin
Wu, Guohua
Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere
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
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4070580/
https://www.ncbi.nlm.nih.gov/pubmed/25003147
http://dx.doi.org/10.1155/2014/697132
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AT wuguohua gapphenomenonofanabstractwillmoretypefunctionalofhypersurfaceinunitsphere

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