English

Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces

Analysis of PDEs 2017-02-10 v3 Spectral Theory

Abstract

We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary. The argument involves frequency function methods for harmonic functions in the interior of the surface as well as the construction of exponentially accurate approximations for the Steklov eigenfunctions near the boundary.

Keywords

Cite

@article{arxiv.1506.07600,
  title  = {Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces},
  author = {Iosif Polterovich and David A. Sher and John A. Toth},
  journal= {arXiv preprint arXiv:1506.07600},
  year   = {2017}
}

Comments

29 pages, 1 figure. Version 3: some minor changes, final pre-publication version