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.
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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.
| Type: | Article |
|---|---|
| Title: | On the growth of eigenfunction averages: Microlocalization and geometry |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1215/00127094-2019-0020 |
| Publisher version: | http://doi.org/10.1215/00127094-2019-0020 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10087655 |
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