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arXiv · 2401.10505

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

Kui Wang·Shaoheng Zhang
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Abstract

We study the first nonzero eigenvalues for the $p$-Laplacian on quaternionic K\"ahler manifolds. Our first result is a lower bound for the first nonzero closed (Neumann) eigenvalue of the $p$-Laplacian on compact quaternionic K\"ahler manifolds. Our second result is a lower bound for the first Dirichlet eigenvalue of the $p$-Laplacian on compact quaternionic K\"ahler manifolds with smooth boundary. Our results generalize corresponding results for the Laplacian eigenvalues on quaternionic K\"ahler manifolds proved in [22].

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Kui Wang, Shaoheng Zhang. 2024-01-19. Lower bounds for the first eigenvalue of the $p$-Laplacian on quaternionic K\"ahler manifolds. https://arxiv.org/abs/2401.10505

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