摘要
研究了Ricci曲率有下界的紧致有边Riemann 流形上Laplace算子的特征值。运用极值原理在Dirichlet边值条件和Robin边值条件下分别作第一特征值的内蕴估计。此外,对于S^n中的极小嵌入紧致超曲面,Yau提出它的第一特征值是否为n-1的问题。把Choi和 Wang对此问题的结果推进一步。
The n-dimension compact Riemannian manifold M with boundary M≠φis considered and the Ricci curvature of M is bounded from below. Some estimates of the first eigenvalue of M are obtained by means of the maximun principle and the gradient estimates of the first eigenfunction. Furthermore, the following problem suggested by S.T. Yau is considered: Is it true that the first eigenvalue for the Laplace-Beltrami operator on an embedded minimal hypersurface of S is n-1? The result λ1≥n-1/2 is obtained.
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
1990年第1期19-23,共5页
Journal of Xiamen University：Natural Science
