Defect measures of eigenfunctions with maximal L growth
Annales de l'Institut Fourier, Volume 69 (2019) no. 4, p. 1757-1798

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.

Nous caractérisons les mesures de défauts de séquences de fonctions propres de Laplace avec croissance L maximale. En conséquence, nous obtenons des nouvelles preuves de résultats sur la géométrie des variétés avec une croissance des fonctions propres maximale obtenus par Sogge–Toth–Zelditch, et nous généralisons ceux de Sogge–Zelditch au cas lisse. Nous obtenons également une dépendance géométrique explicite de la constante de Hörmander L liée aux functions propres de haute énergie, améliorant les estimations de Donnelly.

Received : 2017-08-31
Revised : 2018-02-13
Accepted : 2018-07-12
Published online : 2019-09-16
DOI : https://doi.org/10.5802/aif.3281
Classification:  35P20,  58J50
Keywords: eigenfunctions, defect measures, sup-norms
@article{AIF_2019__69_4_1757_0,
     author = {Galkowski, Jeffrey},
     title = {Defect measures of eigenfunctions with maximal $L^\infty $ growth},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {69},
     number = {4},
     year = {2019},
     pages = {1757-1798},
     doi = {10.5802/aif.3281},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2019__69_4_1757_0}
}
Defect measures of eigenfunctions with maximal $L^\infty $ growth. Annales de l'Institut Fourier, Volume 69 (2019) no. 4, pp. 1757-1798. doi : 10.5802/aif.3281. https://aif.centre-mersenne.org/item/AIF_2019__69_4_1757_0/

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