# Article

MSC: 53C24, 53C40
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Keywords:
Extremal functional; Mean curvature; Totally umbilical
Summary:
Let $M$ be an $n$-dimensional submanifold in the unit sphere $S^{n+p}$, we call $M$ a $k$-extremal submanifold if it is a critical point of the functional $\int _M\rho ^{2k}\,\mathrm{d}v$. In this paper, we can study gap phenomenon for these submanifolds.
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