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

Christianson, Hans; Hassell, Andrew; Toth, John A.


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...[Show more]

CollectionsANU Research Publications
Date published: 2015
Type: Journal article
Source: International Mathematics Research Notices
DOI: 10.1093/imrn/rnt342


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