Algèbres de Royden et homéomorphismes à p-dilatation bornée entre espaces métriques mesurés

The goal of this thesis is to introduce the notions of Royden algebra and mapping with bounded p-dilation between metric measure spaces. In particular, we give sufficient conditions for a metric measure space to be characterized, up to bilipschitz equivalence, by its Royden algebra. We also study sufficient conditions for mapping with bounded p-dilation between metric measure spaces to be a quasi-isometry or to be a lipschitiz map. Our results are obtained in the framework of the theory of axiomatic Sobolev spaces on metric measure spaces and are thus of a very general nature. However, we show that the application of these results to the particular case of nilpotent Lie groups with a Hörmander system gives new concrete information on the geometry of these groups.

    Thèse École polytechnique fédérale de Lausanne EPFL, n° 2422 (2001)
    Faculté des sciences de base
    Jury: Thierry Coulhon, Vladimir Gol'dshtein, Kathryn Hess Bellwald, Pierre Pansu, Charles Stuart

    Public defense: 2001-7-12


    Record created on 2005-03-16, modified on 2016-08-08

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