title: Gap phenomenon of an abstract Willmore type functional of hypersurface in unit sphere.
abstract: 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.
authors.affiliation: College of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, China.
authors.forename: Yanqi
authors.initials: Y
authors.lastname: Zhu
authors.affiliation: College of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, China.
authors.forename: Jin
authors.initials: J
authors.lastname: Liu
authors.affiliation: College of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, China.
authors.forename: Guohua
authors.identifier: 0000-0003-1552-9620
authors.initials: G
authors.lastname: Wu
mesh_terms: D055641:Mathematical Concepts