Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces
Iosif Polterovich, David A. Sher, John A. Toth
TL;DR
This paper establishes precise bounds on the length of nodal lines of Steklov eigenfunctions on real-analytic surfaces, using advanced harmonic analysis and approximation techniques.
Contribution
It provides the first sharp bounds for the nodal length of Steklov eigenfunctions on real-analytic surfaces with boundary.
Findings
Sharp upper and lower bounds for nodal length
Use of frequency function methods for harmonic functions
Construction of exponentially accurate approximations near boundary
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.
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