Galkowski, J;
(2019)
A microlocal approach to eigenfunction concentration.
Journées Équations aux dérivées partielles
, 2018
, Article 3. 10.5802/jedp.663.
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Abstract
We describe a new approach to understanding averages of high energy Laplace eigenfunctions, uh, over submanifolds, ∣∣∣∫HuhdσH∣∣∣ where H⊂M is a submanifold and σH the induced by the Riemannian metric on M. This approach can be applied uniformly to submanifolds of codimension 1≤k≤n and in particular, gives a new approach to understanding ∥uh∥L∞(M). The method, developed in [4, 5, 6, 7, 12, 13], relies on estimating averages by the behavior of uh microlocally near the conormal bundle to H. By doing this, we are able to obtain quantitative improvements on eigenfunction averages under certain uniform non-recurrent conditions on the conormal directions to H. In particular, we do not require any global assumptions on the manifold (M,g).
| Type: | Article |
|---|---|
| Title: | A microlocal approach to eigenfunction concentration |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.5802/jedp.663 |
| Publisher version: | https://doi.org/10.5802/jedp.663 |
| 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 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-pp.ucl.ac.uk/id/eprint/10138603 |
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