伪黎曼空间L_p^(n+p)中紧致类空子流形上的积分不等式

Integral Inequalities for the Compact Space-like Sub-manifold in Pseudo-Riemannian space L_p^(n+p)

设L_p^(n+p)是截面曲率KL满足条件KL≥a(a是实数)的伪黎曼空间,Mn(n≥2)是L_p^(n+p)中的紧致类空子流形.本文得到了Mn上Laplacian算子的第一特征值的两个积分不等式.

Let Lp^n＋p be a Pseudo-Riemannian space with sectional curvature KL satisfy KL≥a,LetM^n（n≥2）be compact space-like submanifold in Lp^n＋p .we obtain two integral inequalities for the first eigenvalue λ1 of Laplacian on M^n.