LOWER BOUNDS FOR THE FIRST EIGENVALUE OF p-LAPLACIAN ON KAHLER MANIFOLDS

We study first nonzero eigenvalues for the p-Laplacian on Ka.hler manifolds. Our first result is a lower bound for the first nonzero closed (Neu-mann) eigenvalue of the p-Laplacian on compact Ka.hler manifolds in terms of dimension, diameter, and lower bounds of holomorphic sectional curvature and orthogonal Ricci curvature for p is an element of (1, 2]. Our second result is a sharp lower bound for the first Dirichlet eigenvalue of the p-Laplacian on compact Ka.hler manifolds with smooth boundary for p is an element of (1, infinity). Our results generalize corresponding results for the Laplace eigenvalues on Ka.hler manifolds proved by Li and Wang [Trans. Amer. Math. Soc. 374 (2021), pp. 8081-8099].