关于拟常曲率空间的紧致极小子流形的积分不等式

About some integrate inequalities on compact minimal submanifolds in Riemannian manifold of quasi constant curvature

给出了拟常曲率空间紧致极小子流形的两个积分不等式，推广了前人在常曲率空间的相应结果．即：∫ＭＳ〔ｐｎ（ｃ－２Ｋ）－Ｓ〕ｄＶ≥０，当Ｋ≤０时有∫ＭＳ〔ｐｎ（ｃ－Ｋ）－Ｓ〕ｄＶ≥０；

Two integrate inequalities on compact minimal submanifolds in Riemannian manifold of quasi constant curvature are given. A wide use is made of the theorems put forward by former researchers on the space as a constant curvature space form, i.e. ∫ M S pn(c-2K)-S d V ≥0, when K ≤0, ∫ MS pn(c-K)-S d V ≥0; ∫ MS (2-1/p)S-n d V ≥0.