Gradient estimate of a Neumann eigenfunction on a compact manifold with boundary

Jingchen Hu, Yiqian Shi, Bin Xu

Let $e_{ł}(x)$ be a Neumann eigenfunction with respect to the positive Laplacian $\Delta$ on a compact Riemannian manifold $M$ with boundary such that $\Delta e_{ł}={ł}^2{e}_{ł}$ in the interior of…