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

Hans Christianson; Andrew Hassell; John A. Toth

doi:10.1093/imrn/rnt342

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

Hans Christianson, Andrew Hassell^*, John A. Toth

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

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_h, (h²δ - 1)φ_h = 0, to H in the region exterior to the coball bundle of H, on h^δ-scales (0 ≤ δ ≤ ²₃). 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.

Original language	English
Pages (from-to)	1638-1665
Number of pages	28
Journal	International Mathematics Research Notices
Volume	2015
Issue number	6
DOIs	https://doi.org/10.1093/imrn/rnt342
Publication status	Published - 2015

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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 φh, (h2δ - 1)φh = 0, to H in the region exterior to the coball bundle of H, on hδ-scales (0 ≤ δ ≤ 23). 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 Schr{\"o}dinger operators.",

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AU - Hassell, Andrew

AU - Toth, John A.

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PY - 2015

Y1 - 2015

N2 - 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 φh, (h2δ - 1)φh = 0, to H in the region exterior to the coball bundle of H, on hδ-scales (0 ≤ δ ≤ 23). 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.

AB - 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 φh, (h2δ - 1)φh = 0, to H in the region exterior to the coball bundle of H, on hδ-scales (0 ≤ δ ≤ 23). 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.

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DO - 10.1093/imrn/rnt342

M3 - Article

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EP - 1665

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 6

ER -

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

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