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H 1 Differential forms and the Hölder equivalence problem - Part 1

Auteurs : Pansu, Pierre (Auteur de la Conférence)
CIRM (Editeur )

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Heisenberg group sub-Riemannian distance metric geometry contact structure bi-Lipschitz homeomorphism bi-Lipschitz embedding Banach space quantitative differentiability von Koch snowflake Assouad dimension Hölder homeomorphism Hausdorff dimension sectional curvature pinching CR geometry ideal boundary (hyperbolic) quasisymmetric mapping

Résumé : A sub-Riemannian distance is obtained when minimizing lengths of paths which are tangent to a distribution of planes. Such distances differ substantially from Riemannian distances, even in the simplest example, the 3-dimensional Heisenberg group. This raises many questions in metric geometry: embeddability in Banach spaces, bi-Lipschitz or bi-Hölder comparison of various examples. Emphasis will be put on Gromov's results on the Hölder homeomorphism problem, and on a quasisymmetric version of it motivated by Riemannian geometry.

Codes MSC :
53C15 - General geometric structures on manifolds (almost complex, contact, symplectic, almost product structures, etc.)
53C20 - Global Riemannian geometry, including pinching, See Also { 31C12, 58B20}

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 09/09/14
    Date de captation : 01/09/14
    Collection : Research talks ; Geometry
    Format : QuickTime (.mov) Durée : 01:21:59
    Domaine : Geometry
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2014-09-01_Pansu.mp4

Informations sur la rencontre

Nom de la rencontre : Sub-Riemannian manifolds : from geodesics to hypoelliptic diffusion / Géométrie sous-riemannienne : des géodésiques aux diffusions hypoelliptiques
Organisateurs de la rencontre : Agrachev, Andrei A. ; Boscain, Ugo ; Jean, Frédéric ; Sigalotti, Mario
Dates : 01/09/14 - 05/09/14
Année de la rencontre : 2014
URL Congrès : http://www.cmap.polytechnique.fr/subriem...

Citation Data

DOI : 10.24350/CIRM.V.18559803
Cite this video as: Pansu, Pierre (2014). Differential forms and the Hölder equivalence problem - Part 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18559803
URI : http://dx.doi.org/10.24350/CIRM.V.18559803

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