Troyanov, MarcGafaiti, Khaled2005-03-162005-03-162005-03-16200110.5075/epfl-thesis-2422https://infoscience.epfl.ch/handle/20.500.14299/211323The 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.frthesis::doctoral thesis