Lower bounds for the first eigenvalue of $p$-Laplacian on K\'ahler manifolds

Autor:	Wang, Kui, Zhang, Shaoheng
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs Mathematics - Spectral Theory 35P15 53C55
Druh dokumentu:	Working Paper
Popis:	We study the eigenvalue problem for the $p$-Laplacian on K\"ahler manifolds. Our first result is a lower bound for the first nonzero eigenvalue of the $p$-Laplacian on compact K\"ahler 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 K\"ahler manifolds with smooth boundary for $p\in (1, \infty)$. Our results generalize corresponding results for the Laplace eigenvalues on K\"ahler manifolds proved in [14]. Comment: All comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2209.10713 Zobrazit plný text záznamu View this record from Arxiv