The Steklov spectrum of surfaces: asymptotics and invariants

Author:

GIROUARD ALEXANDRE,PARNOVSKI LEONID,POLTEROVICH IOSIF,SHER DAVID A.

Abstract

AbstractWe 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 27 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Applications of possibly hidden symmetry to Steklov and mixed Steklov problems on surfaces;Journal of Mathematical Analysis and Applications;2024-06

2. Some recent developments on the Steklov eigenvalue problem;Revista Matemática Complutense;2023-09-28

3. Weyl’s Law for the Steklov Problem on Surfaces with Rough Boundary;Archive for Rational Mechanics and Analysis;2023-08-10

4. A Meyer–Vietoris Formula for the Determinant of the Dirichlet-to-Neumann Operator on Riemann Surfaces;The Journal of Geometric Analysis;2022-12-19

5. Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons;Proceedings of the London Mathematical Society;2022-06-13

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