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

Kui Wang; Shaoheng Zhang

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arXiv · 2209.10713

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

Kui Wang·Shaoheng Zhang

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Abstract

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].

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BibTeX RIS

Kui Wang, Shaoheng Zhang. 2022-09-22. Lower bounds for the first eigenvalue of $p$-Laplacian on K\"ahler manifolds. https://arxiv.org/abs/2209.10713

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