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<https://discovery.ucl.ac.uk/id/eprint/10087655> <http://purl.org/dc/terms/title> "On the growth of eigenfunction averages: Microlocalization and geometry"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10087655> <http://purl.org/ontology/bibo/abstract> "Let (M,g) be a smooth, compact Riemannian manifold, and let {φ_{h]} be an L²  -normalized sequence of Laplace eigenfunctions, -h²Δ_{g}φ_{h} = φ_{h}. Given a smooth submanifold H ⊂ M of codimension K ≥ 1, we find conditions on the pair ({φ_{h}, H) for which |∫_{H}φ_{h} δσ_{H}| = o (h\\frac{1-k}{2}), h→0⁺.  One such condition is that the set of conormal directions to H  that are recurrent has measure 0. In particular, we show that the upper bound holds for any H if (M, g) is a surface with Anosov geodesic flow or a manifold of constant negative curvature. The results are obtained by characterizing the behavior of the defect measures of eigenfunctions with maximal averages."^^<http://www.w3.org/2001/XMLSchema#string> .
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