Integral Inequality Of Minimal Curvature Submanifolds

Submanifolds are closely related to many disciplines,which has certain practical significance.Let Mn is closed minimal curvature submanifolds of Nn+p,where Nn+p is hypersurface of Rn+p+1 in this paper.If the principal curvature |λ|≥ c(c>0),then we have ∫Mn[np(c2-2K)-S]SdV>0,where K(x)is the function assigns to each point of Mn the infinimum of the sectional curvatures of Mn at that point and S is the length of the second fundamental form of Mn,in particular,if K(x)≤0 for(?)x∈Mn,we have ∫Mn[np(c2-K)-S]SdV≥0.This result extends the conclusion of Yau[21]in 1974.