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 $$H^{n-1}(N_{\lambda })\ge C{\lambda }^{\frac{3-n}{2}}$$ for some positive constant $C$ depending only on the manifold.

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• Lower bounds for interior nodal sets of Steklov eigenfunctions