Density of zero sets for sums of eigenfunctions

Abstract

We consider linear combinations of eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold (M, g) and investigate a density property of their zero sets. More precisely, let where Denoting by Zf the zero-set of f, we show that for any The proof is based on a new integral Harnack-type estimate for positive solutions of higher order elliptic PDEs.