Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces

摘要

We prove sharp upper and lower bounds for the nodal length of Stekloveigenfunctions on real-analytic Riemannian surfaces with boundary. The argumentinvolves frequency function methods for harmonic functions in the interior ofthe surface as well as the construction of exponentially accurateapproximations for the Steklov eigenfunctions near the boundary.