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H 1 Boundary calculus on conformally compact manifolds, and a boundary Yamabe problem

Auteurs : Gover, A. Rod (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : On conformally compact manifolds of arbitrary signature I will describe a natural boundary calculus for computing the asymptotics of a class of natural boundary problems. This is applied to the non-linear problem of finding, conformally, a conformally compact constant scalar curvature metric on the interior of a manifold with boundary. This problem was studied from a different point of view by Andersson, Chrusciel, Friedrich (ACF) in 1992. They identified a conformal submanifold invariant that obstructs smooth boundary asymptotics for the problem on 3-manifolds (and gave some information on the obstructions in other dimensions). This invariant is the same as that arising from the variation of the Willmore energy. We find higher order submanifold invariants that generalise that curvature quantity found by ACF. This construction also leads to a route for manufacturing large classes of other conformal submanifold invariants.

    Codes MSC :
    53C20 - Global Riemannian geometry, including pinching, See Also { 31C12, 58B20}
    58J05 - elliptic equations on manifolds - general theory

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 08/10/14
      Date de captation : 06/10/14
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : quicktime ; audio/x-aac
      Durée : 00:55:11
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-10-06_Gover.mp4

    Informations sur la rencontre

    Nom de la rencontre : Spin geometry and analysis on manifolds / Géométrie spinorielle et analyse sur les variétés
    Organisateurs de la rencontre : Ginoux, Nicolas ; Humbert, Emmanuel ; Lawn, Marie-Amélie ; Moroianu, Andrei
    Dates : 06/10/14 - 10/10/14
    Année de la rencontre : 2014

    Citation Data

    DOI : 10.24350/CIRM.V.18603603
    Cite this video as: Gover, A. Rod (2014). Boundary calculus on conformally compact manifolds, and a boundary Yamabe problem. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18603603
    URI : http://dx.doi.org/10.24350/CIRM.V.18603603


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