Restriction of Toral Eigenfunctions to Hypersurfaces and Nodal Sets
نویسندگان
چکیده
We give uniform upper and lower bounds for the L 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.
منابع مشابه
On the nodal sets of toral eigenfunctions
We study the nodal sets of eigenfunctions of the Laplacian on the standard d-dimensional flat torus. The question we address is: Can a fixed hypersurface lie on the nodal sets of eigenfunctions with arbitrarily large eigenvalue? In dimension two, we show that this happens only for segments of closed geodesics. In higher dimensions, certain cylindrical sets do lie on nodal sets corresponding to ...
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