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

Kui Wang; Shaoheng Zhang

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

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arxiv 2401.10505 v1 pith:ESU6CVSO submitted 2024-01-19 math.DG math.AP

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

Kui Wang , Shaoheng Zhang This is my paper

classification math.DG math.AP

keywords ahlerfirstlaplacianmanifoldsquaternioniceigenvaluelowerbound

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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].

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

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