THE STEKLOV SPECTRUM OF SURFACES: ASYMPTOTICS AND INVARIANTS
Alexandre Girouard, Leonid Parnovski, Iosif Polterovich, David, A. Sher · 2014
Abstract. We obtain precise asymptotics for the Steklov eigenvalues on a compact Rie-mannian surface with boundary. It is shown that the number of connected components of the boundary, as well as their lengths, are invariants of the Steklov spectrum. The proofs are based on pseudodifferential techniques for the Dirichlet-to-Neumann operator and on a number–theoretic argument. 1. Introduction and