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 |?|? 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.