**Title:** $L^2$ restriction bounds for eigenfunction Neumann data along hypersurfaces

**Speaker:** John Toth

**Speaker Info:** McGill University

**Brief Description:**

**Special Note**:

**Abstract:**

Let $(M,g)$ be a compact, Riemannian manifold, $H$ be a smooth oriented hypersurface with unit exterior normal $nu$ and $phi_{lambda_j}; j=1,2,...$ be $L^2$-normalized Laplace eigenfunctions with $Delta_g phi_{lambda} + lambda^2 phi_{lambda} =0.$ We consider the eigenfunction Neumann data $phi_{lambda}^{H,nu}:= frac{1}{lambda} partial_{nu} phi_{lambda} |_{H}$ along H and prove that $$ | phi_{lambda}^{H,nu} |_{L^2(H)} = O(1).$$These estimates also extend to more general semiclassical Schr"{o}dinger operators. This is joint work with Hans Christianson and Andrew Hassell.

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