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arXiv · 1303.4319

Exterior mass estimates and $L^2$ restriction bounds for Neumann data along hypersurfaces

Hans Christianson·Andrew Hassell·John A. Toth
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Abstract

We study the problem of estimating the $L^2$ 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 $ϕ_h$, $(h^2 Δ- 1)ϕ_h = 0$, to $H$ in the region exterior to the coball bundle of $H$, on $h^δ$-scales ($0\leq δ< 2/3$). We use this estimate to obtain an $O(1)$ $L^2$-restriction bound for the Neumann data along $H.$ The estimate also applies to eigenfunctions of semiclassical Schrödinger operators.

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Hans Christianson, Andrew Hassell, John A. Toth. 2013-11-08. Exterior mass estimates and $L^2$ restriction bounds for Neumann data along hypersurfaces. https://arxiv.org/abs/1303.4319

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