A lower bound for the nodal sets of Steklov eigenfunctions

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 $N_λ$ be its nodal set. Assume that zero is a regular value of Steklov eigenfunctions. We show that $H^{n-1}(N_λ)\geq Cλ^{\frac{3-n}{2}}$ for some positive constant $C$ depending only on the manifold.

No reviews yet.

No comments yet.