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arXiv · 1705.09595

Averages of eigenfunctions over hypersurfaces

Yaiza Canzani·Jeffrey Galkowski·John A. Toth
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Abstract

Let $(M,g)$ be a compact, smooth, Riemannian manifold and $\{ \phi_h \}$ an $L^2$-normalized sequence of Laplace eigenfunctions with defect measure $\mu$. Let $H$ be a smooth hypersurface. Our main result says that when $\mu$ is $\textit{not}$ concentrated conormally to $H$, the eigenfunction restrictions to $H$ and the restrictions of their normal derivatives to $H$ have integrals converging to 0 as $h \to 0^+$.

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Yaiza Canzani, Jeffrey Galkowski, John A. Toth. 2017-05-26. Averages of eigenfunctions over hypersurfaces. https://doi.org/10.1007/s00220-017-3081-9

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