English
Understanding the growth of Laplace eigenfunctions (part 1 of 2)
Post-edited
Auteurs : Canzani, Yaiza (Auteur de la Conférence)
CIRM (Editeur )
35P20 - Asymptotic distribution of eigenvalues and eigenfunctions for PD operators
53C21 - Methods of Riemannian geometry, including PDE methods; curvature restrictions
53C22 - Geodesics [See also 58E10]
53C40 - Global submanifolds [See also 53B25]
58J50 - Spectral problems; spectral geometry; scattering theory
CIRM (Editeur )
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| Laplace eigenfunctions supremum of eigenfunctions conjugate points geodesic beams tubes decomposition average of eigenfunctions |
Résumé :
In this talk we will discuss a new geodesic beam approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of $L^{2}$ mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Using the description of concentration, we obtain quantitative improvements on the known bounds in a wide variety of settings.
Codes MSC : 35P20 - Asymptotic distribution of eigenvalues and eigenfunctions for PD operators
53C21 - Methods of Riemannian geometry, including PDE methods; curvature restrictions
53C22 - Geodesics [See also 58E10]
53C40 - Global submanifolds [See also 53B25]
58J50 - Spectral problems; spectral geometry; scattering theory
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 03/06/2019 Date de captation : 08/05/2019 Sous collection : Research talks arXiv category : Analysis of PDEs ; Spectral Theory Domaine : PDE ; Geometry Format : MP4 (.mp4) - HD Durée : 00:48:57 Audience : Researchers Download : https://videos.cirm-math.fr/2019-05-08_Canzani.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Méthodes microlocales en analyse et géométrie / Microlocal Methods in Analysis and GeometryOrganisateurs de la rencontre : Carron, Gilles ; Mazzeo, Rafe ; Piazza, Paolo ; Wunsch, Jared Dates : 06/05/2019 - 10/05/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/1988.html
Données de citation
DOI : 10.24350/CIRM.V.19521503Citer cette vidéo: Canzani, Yaiza (2019). Understanding the growth of Laplace eigenfunctions (part 1 of 2). CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19521503 URI : http://dx.doi.org/10.24350/CIRM.V.19521503 |
Voir aussi
- [Multi angle] Emergence of the quantum wave equation in classical deterministic hyperbolic dynamics / Auteur de la Conférence Faure, Frédéric.
- [Multi angle] ALC manifolds with exceptional holonomy / Auteur de la Conférence Foscolo, Lorenzo.
- [Multi angle] Linear stability of slowly rotating Kerr spacetimes / Auteur de la Conférence Hintz, Peter.
- [Multi angle] Geodesic beams in eigenfunction analysis (part 2 of 2) / Auteur de la Conférence Galkowski, Jeffrey.
Bibliographie
- Canzani, Y., & Galkowski, J. (2019). Eigenfunction concentration via geodesic beams. arXiv preprint arXiv:1903.08461. - https://arxiv.org/abs/1903.08461
- Canzani, Y., & Galkowski, J. (2018). A Novel Approach to Quantitative Improvements for Eigenfunction Averages. arXiv preprint arXiv:1809.06296. - https://arxiv.org/abs/1809.06296
- Canzani, Y., & Galkowski, J. (2017). On the growth of eigenfunction averages: microlocalization and geometry. arXiv preprint arXiv:1710.07972. - https://arxiv.org/abs/1710.07972
- Canzani, Y., Galkowski, J., & Toth, J. A. (2018). Averages of eigenfunctions over hypersurfaces. Communications in Mathematical Physics, 360(2), 619-637. - https://arxiv.org/abs/1705.09595
