Nodal sets of Steklov eigenfunctions near the boundary

A Steklov eigenfunction is a harmonic function in a bounded domain whose normal derivative at the boundary is proportional to the function itself. I will discuss the zero sets of such functions: a nice property is that there are many zeros near the boundary. I will talk about some lower and upper bounds for the Hausdorff measure of the zero set; several questions remain unanswered. Comparisons with the (slightly) better understood case of eigenfunctions of the Laplace-Beltrami operator will also be provided.