Degenerating sequences of conformal classes and the conformal Steklov spectrum

Abstract Let $\Sigma $ be a compact surface with boundary. For given conformal class c on the functional $\sigma _k^*(\Sigma ,c)$ is defined as supremum of k th normalized Steklov eigenvalue over all metrics in . We consider behavior this moduli space classes A precise formula for limit ,c_n)$ when sequence $\{c_n\}$ degenerates obtained. apply to study natural analogs Friedlander–Nadirashvili invariants closed manifolds $\inf _{c}\sigma , where infimum taken show that these quantities are equal $2\pi k$ any As an application our techniques we obtain new estimates nonorientable terms its genus and number boundary components.