The Steklov spectrum of surfaces: asymptotics and invariants

Abstract

We obtain precise asymptotics for the Steklov eigenvalues on a compact Riemannian 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.

10 pages

Cited by in corpus (3)

• Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons
• Optimization of Steklov-Neumann eigenvalues
• Inverse Steklov spectral problem for curvilinear polygons