Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces

2015/06/25 by Iosif Polterovich, Polterovich, Iosif, David A. Sher +3 · 1 citation
Mathematics · #35P20 #58J50 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP #msc:35P20 #msc:58J50

paper · pdf · doi:10.48550/arxiv.1506.07600

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

arxiv created 2017/02/09 · arxiv updated 2017/02/10

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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• Layer Potential Methods for Doubly-Periodic Harmonic Functions

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