Galkowski, J;
(2019)
DEFECT MEASURES OF EIGENFUNCTIONS WITH MAXIMAL L-infinity GROWTH.
Annales de l'Institut Fourier
, 69
(4)
pp. 1757-1798.
10.5802/aif.3281.
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Abstract
We characterize the defect measures of sequences of Laplace eigenfunctions with maximal L∞ growth. As a consequence, we obtain new proofs of results on the geometry of manifolds with maximal eigenfunction growth obtained by Sogge–Toth–Zelditch, and generalize those of Sogge–Zelditch to the smooth setting. We also obtain explicit geometric dependence on the constant in Hörmander’s L∞ bound for high energy eigenfunctions, improving on estimates of Donnelly.
| Type: | Article |
|---|---|
| Title: | DEFECT MEASURES OF EIGENFUNCTIONS WITH MAXIMAL L-infinity GROWTH |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.5802/aif.3281 |
| Publisher version: | https://doi.org/10.5802/aif.3281 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution - Pas de Modification 3.0 France (CC BY-ND 3.0 FR). The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit https://creativecommons.org/licenses/by-nd/3.0/fr/ |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, eigenfunctions, defect measures, sup-norms, KAKEYA-NIKODYM BOUNDS, RIEMANNIAN-MANIFOLDS, SPECTRAL-FUNCTION |
| 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/10083613 |
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