Improvements for eigenfunction averages: An application of geodesic beams

Yaiza Canzani, Jeffrey Galkowski

Let $(M,g)$ be a smooth, compact Riemannian manifold and $\{{\varphi }_{\lambda }\}$ an $L^2$-normalized sequence of Laplace eigenfunctions, $-{\Delta }_g{\varphi }_{\lambda }={\lambda }^2{\varphi }_{\lambda }$. Given a smooth submanifold $H \subset…