Nodal sets of Laplace eigenfunctions: estimates of the Hausdorff measure in dimension two and three

Alexander Logunov, Eugenia Malinnikova

Let ${\Delta }_M$ be the Laplace operator on a compact $n$-dimensional Riemannian manifold without boundary. We study the zero sets of its eigenfunctions $u:\Delta u+\lambda u=0$. In dimension $n=2$…