Lower bounds for the first eigenvalue of the $p$-Laplacian on quaternionic Kähler manifolds

Abstract

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

All comments are welcome! arXiv admin note: text overlap with arXiv:2209.10713