Restriction of toral eigenfunctions to hypersurfaces and nodal sets

Details Restriction of toral eigenfunctions to hypersurfaces and nodal sets Restriction of toral eigenfunctions to hypersurfaces and nodal sets

2011-04-29

arxiv.org/abs/1105.0018v2

Mathematics

Analysis of PDEs

4 figures. v2: Minor revision. Accepted for publication in GAFA

Scientific paper

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.

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