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arXiv · 1911.04596

Sharp lower bound for the first eigenvalue of the Weighted $p$-Laplacian II

Xiaolong Li·Kui Wang
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Abstract

Combined with our previous work \cite{LW19eigenvalue}, we prove sharp lower bound estimates for the first nonzero eigenvalue of the weighted $p$-Laplacian with $1< p< \infty$ on a compact Bakry-\'Emery manifold $(M^n,g,f)$, without boundary or with a convex boundary and Neumann boundary condition, satisfying $\text{Ric}+\nabla^2 f \geq \kappa \, g$ for some $\kappa \in \mathbb{R}$.

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Xiaolong Li, Kui Wang. 2019-11-11. Sharp lower bound for the first eigenvalue of the Weighted $p$-Laplacian II. https://arxiv.org/abs/1911.04596

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