Displaying similar documents to “Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields”

Homogeneous Carnot groups related to sets of vector fields

Andrea Bonfiglioli (2004)

Bollettino dell'Unione Matematica Italiana

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In this paper, we are concerned with the following problem: given a set of smooth vector fields on , we ask whether there exists a homogeneous Carnot group such that is a sub-Laplacian on . We find necessary and sufficient conditions on the given vector fields in order to give a positive answer to the question. Moreover, we explicitly construct the group law i as above, providing direct proofs. Our main tool is a suitable version of the Campbell-Hausdorff formula. Finally, we...

Some relations among volume, intrinsic perimeter and one-dimensional restrictions of functions in Carnot groups

Francescopaolo Montefalcone (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let be a -step Carnot group. The first aim of this paper is to show an interplay between volume and -perimeter, using one-dimensional horizontal slicing. What we prove is a kind of Fubini theorem for -regular submanifolds of codimension one. We then give some applications of this result: slicing of functions, integral geometric formulae for volume and -perimeter and, making use of a suitable notion of convexity, called, we state a Cauchy type formula for -convex sets. Finally,...