Français
Understanding the growth of Laplace eigenfunctions (part 1 of 2)
Post-edited
Authors : Canzani, Yaiza (Author of the conference)
CIRM (Publisher )
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 (Publisher )
Loading the player...
|
| Laplace eigenfunctions supremum of eigenfunctions conjugate points geodesic beams tubes decomposition average of eigenfunctions |
Abstract :
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.
MSC Codes : 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
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 03/06/2019 Conference Date : 08/05/2019 Subseries : Research talks arXiv category : Analysis of PDEs ; Spectral Theory Mathematical Area(s) : PDE ; Geometry Format : MP4 (.mp4) - HD Video Time : 00:48:57 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-05-08_Canzani.mp4 
|
Information on the Event
Event Title : Méthodes microlocales en analyse et géométrie / Microlocal Methods in Analysis and GeometryEvent Organizers : Carron, Gilles ; Mazzeo, Rafe ; Piazza, Paolo ; Wunsch, Jared Dates : 06/05/2019 - 10/05/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/1988.html
Citation Data
DOI : 10.24350/CIRM.V.19521503Cite this video as: 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 |
See Also
- [Multi angle] Emergence of the quantum wave equation in classical deterministic hyperbolic dynamics / Author of the conference Faure, Frédéric.
- [Multi angle] ALC manifolds with exceptional holonomy / Author of the conference Foscolo, Lorenzo.
- [Multi angle] Linear stability of slowly rotating Kerr spacetimes / Author of the conference Hintz, Peter.
- [Multi angle] Geodesic beams in eigenfunction analysis (part 2 of 2) / Author of the conference Galkowski, Jeffrey.
Bibliography
- 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
