H 2 Understanding the growth of Laplace eigenfunctions (part 1 of 2)

Auteurs : Canzani, Yaiza (Auteur de la Conférence)
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

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 03/06/2019
    Date de captation : 08/05/2019
    Collection : Research talks ; Partial Differential Equations ; Geometry
    Format : MP4 (.mp4) - HD
    Durée : 00:48:57
    Domaine : PDE ; Geometry
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2019-05-08_Canzani.mp4

Informations sur la rencontre

Nom de la rencontre : Méthodes microlocales en analyse et géométrie / Microlocal Methods in Analysis and Geometry
Organisateurs 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

Citation Data

DOI : 10.24350/CIRM.V.19521503
Cite 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

Voir aussi


  • 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

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