Lower bounds for the first eigenvalue of $p$-Laplacian on K\'ahler manifolds
Autor: | Wang, Kui, Zhang, Shaoheng |
---|---|
Rok vydání: | 2022 |
Předmět: | |
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: |