双曲空间上有关拉普拉斯二次多项式的特征值估计

Estimates on Eigenvalues for Quadratic Polynomial Operator of the Laplacian on a Hyperbolic Space

考虑双曲空间有界区域上的有关拉普拉斯二次多项式的特征值估计.利用Rayleigh-Ritz公式,得到了用前k个特征值估计第k+1个特征值的特征值万有估计.

Eigenvalues of quadratic polynomial operator of the Laplacian on a bounded domain in a hyperbolic space are studied.Applying the the Rayleigh-Ritz principle,we obtain estimates on the（k＋1）th eigenvalue in terms of the first kth eigenvalue independent of the domains.