# Nodal sets of Steklov eigenfunctions near the boundary

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Stefano Decio, Norwegian University of Science and Technology

We will discuss zero sets of Steklov eigenfunctions: we show that there are many zeros near the boundary and improve on previous bounds for the Hausdorff measure of the zero set; in two dimensions we also show that one can place a ball of wavelength radius inside a nodal domain. Several questions remain unanswered. Comparisons with the (slightly) better understood case of eigenfunctions of the Laplace-Beltrami operator will also be provided.