A lower bound for the nodal sets of Steklov eigenfunctions

Abstract

We consider the lower bound of nodal sets of Steklov eigenfunctions on smooth Riemannian manifolds with boundary--the eigenfunctions of the Dirichlet-to-Neumann map. Let $N_\lambda$ be its nodal set. Assume that zero is a regular value of Steklov eigenfunctions. We show that $$H^{n-1}(N_\lambda)\geq C\lambda^{\frac{3-n}{2}}$$ for some positive constant $C$ depending only on the manifold.