Restriction of toral eigenfunctions to hypersurfaces and nodal sets
Analysis of PDEs
2011-09-23 v2 Mathematical Physics
math.MP
Number Theory
Abstract
We give uniform upper and lower bounds for the L^2 norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. We also present several related results concerning the nodal sets of eigenfunctions.
Cite
@article{arxiv.1105.0018,
title = {Restriction of toral eigenfunctions to hypersurfaces and nodal sets},
author = {Jean Bourgain and Zeev Rudnick},
journal= {arXiv preprint arXiv:1105.0018},
year = {2011}
}
Comments
4 figures. v2: Minor revision. Accepted for publication in GAFA