Hausdorff measure bound for the nodal sets of Neumann Laplace eigenfunctions
Shaghayegh Fazliani · arXiv (Cornell University) · 2023
We study the nodal sets of Neumann Laplace eigenfunctions in a bounded domain with $\mathcal{C}^{1,1}$ boundary. We show that for $u_λ$ such that $Δu_λ+ λu_λ= 0 $ with the Neumann boundary condition $\partial_νu_λ= 0$, we have $\mathcal{H}^{n-1}(\{u_λ= 0\}) \leq C \sqrtλ$.