黎曼流形上散度型算子的低阶特征值估计(英文)

ESTIMATES FOR LOWER ORDER EIGENVALUES FOR OPERATORS IN DIVERGENCE FORM ON RIEMANNIAN MANIFOLDS

本文研究黎曼流形上散度型算子的低阶特征值.利用Rayleigh-Ritz不等式,得到了这种算子的低阶特征值所满足的一个不等式.而且,对于拉普拉斯算子的低阶特征值,本文的结果是最佳的.

Eigenvalues of operators in divergence form with a weight on Riemannian man- ifolds are considered. By the Rayleigh-Ritz inequality, we obtain universal inequalities for lower order eigenvalues of such operators. In particular, for lower order eigenvalues of Laplacian, our results are sharp.