Partial Differential Equations
Restriction of toral eigenfunctions to hypersurfaces

Presented by: Jean Bourgain

Bourgain, Jean1; Rudnick, Zeév1, 2
1 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States
2 Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1249-1253.

Let Td=Rd/Zd be the d-dimensional flat torus. We establish for d=2,3 uniform upper and lower bounds on the restrictions of the eigenfunctions of the Laplacian to smooth hyper-surfaces with non-vanishing curvature.

Soit Td=Rd/Zd le tore plat d-dimensionnel. Pour d=2 et d=3, on établit des bornes supérieures et inférieures uniformes sur les restrictions des fonctions propres de l'opérateur de Laplace–Beltrami à des surfaces lisses de courbure non nulle.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.08.008
Bourgain, Jean 1; Rudnick, Zeév 1, 2

1 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States
2 Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel 
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Bourgain, Jean; Rudnick, Zeév. Restriction of toral eigenfunctions to hypersurfaces. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1249-1253. doi : 10.1016/j.crma.2009.08.008. http://www.numdam.org/articles/10.1016/j.crma.2009.08.008/

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