The Steklov spectrum of surfaces: asymptotics and invariants
A Girouard, L Parnovski, I Polterovich… - … Proceedings of the …, 2014 - cambridge.org
Mathematical Proceedings of the Cambridge Philosophical Society, 2014•cambridge.org
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.
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.
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.
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