黎曼流形上Laplace算子的高阶特征值下界估计
Lower Bound Estimation of Higher Eigenvalues of Laplace Operators on Riemannian Manifold
摘要:
本文研究黎曼流形上Lapalce算子的高阶特征值下界估计，对Ricci曲率具有负下界的黎曼流形，Li-Yau得到了定性的下界估计，本文运用了热核的梯度函数的梯度估计和Harnack不等式的方法，给出了Ricci曲率负下界的黎曼流形上定量的高阶特征值下界估计。
Abstract:
In this paper, we study the lower bound estimates of higher eigenvalues of Lapalce operator on Riemannian manifold. For Riemannian manifolds with negative lower bounds of Ricci curvature, Li-Yau obtained qualitative lower bound estimates. In this paper, we use the method of the gradient estimation of gradient function of the hot kernel and Harnack type inequality; we give the quantitative lower bound estimation of higher eigenvalues on Riemannian manifold with negative lower bound of Ricci curvature.
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