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