论文标题
$ p $ -laplacian在kähler歧管上的第一个特征值的下限
Lower bounds for the first eigenvalue of $p$-Laplacian on Kähler manifolds
论文作者
论文摘要
我们研究了Kähler歧管上$ p $ -laplacian的特征值问题。我们的第一个结果是在紧凑的Kähler歧管上的第一个非零特征值的下限，在尺寸，直径和全体形态截面曲率和正交ricci curvature的尺寸，直径和下限方面是$ p \ in（1，2] $。 $ p $ -laplacian在紧凑型kähler歧管上具有光滑边界的$ p \ in（1，\ infty）$。
We study the eigenvalue problem for the $p$-Laplacian on Kähler manifolds. Our first result is a lower bound for the first nonzero eigenvalue of the $p$-Laplacian on compact Kähler manifolds in terms of dimension, diameter, and lower bounds of holomorphic sectional curvature and orthogonal Ricci curvature for $p\in (1, 2]$. Our second result is a sharp lower bound for the first Dirichlet eigenvalue of the $p$-Laplacian on compact Kähler manifolds with smooth boundary for $p\in (1, \infty)$. Our results generalize corresponding results for the Laplace eigenvalues on Kähler manifolds proved in [14].
