Lower bounds for the first eigenvalue of p-Laplacian on Kähler manifolds

2022/09/22 by Kui Wang, Shaoheng Zhang, Wang, Kui +1 · 1 citation
Mathematics · #35P15 #53C55 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2209.10713

openalex publication_date 2022/09/22 · openalex created_date 2022/09/25 · openalex updated_date 2026/07/28

Abstract

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∈ (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∈ (1, ∞). Our results generalize corresponding results for the Laplace eigenvalues on Kähler manifolds proved in [14].

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