Restriction of toral eigenfunctions to hypersurfaces and nodal sets

Jean Bourgain, Zeév Rudnick*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)878-937
Number of pages60
JournalGeometric and Functional Analysis
Volume22
Issue number4
DOIs
StatePublished - Aug 2012

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