eprintid: 10087655 rev_number: 14 eprint_status: archive userid: 608 dir: disk0/10/08/76/55 datestamp: 2019-12-09 15:01:37 lastmod: 2020-02-12 18:12:07 status_changed: 2019-12-09 15:01:37 type: article metadata_visibility: show creators_name: Canzani, Y creators_name: Galkowski, J title: On the growth of eigenfunction averages: Microlocalization and geometry ispublished: pub divisions: UCL divisions: A01 divisions: B04 divisions: C06 divisions: F59 note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. 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. date: 2019-11 date_type: published publisher: DUKE UNIV PRESS official_url: http://doi.org/10.1215/00127094-2019-0020 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1687951 doi: 10.1215/00127094-2019-0020 lyricists_name: Galkowski, Jeffrey Eric lyricists_id: JGALK87 actors_name: Kalinowski, Damian actors_id: DKALI47 actors_role: owner full_text_status: public publication: Duke Mathematical Journal volume: 168 number: 16 pagerange: 2991-3055 pages: 65 citation: Canzani, Y; Galkowski, J; (2019) On the growth of eigenfunction averages: Microlocalization and geometry. Duke Mathematical Journal , 168 (16) pp. 2991-3055. 10.1215/00127094-2019-0020 <https://doi.org/10.1215/00127094-2019-0020>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10087655/1/Galkowski_On%20the%20growth%20of%20eigenfunction%20averages.%20Microlocalization%20and%20geometry_AAM.pdf