Exterior mass estimates and L2-restriction bounds for neumann data along hypersurfaces

Abstract

We study the problem of estimating the L2-norm of Laplace eigenfunctions on a compact Riemannian manifold M when restricted to a hypersurface H. We prove mass estimates for the restrictions of eigenfunctions φ<inf>h</inf>, (h2δ - 1)φ<inf>h</inf> = 0, to H in the region exterior to the coball bundle of H, on hδ-scales (0 ≤ δ ≤ 2<inf>3</inf>). We use this estimate to obtain an O(1) L2-restriction bound for the Neumann data along H. The estimate also applies to eigenfunctions of semiclassical Schrödinger operators. Show more