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Degree theory for VMO maps on metric spaces

Francesco UguzzoniErmanno Lanconelli — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We construct a degree theory for Vanishing Mean Oscillation functions in metric spaces, following some ideas of Brezis & Nirenberg. The underlying sets of our metric spaces are bounded open subsets of N and their boundaries. Then, we apply our results in order to analyze the surjectivity properties of the L -harmonic extensions of VMO vector-valued functions. The operators L we are dealing with are second order linear differential operators sum of squares of vector fields satisfying the hypoellipticity...

A note on lifting of Carnot groups.

Andrea BonfiglioliFrancesco Uguzzoni — 2005

Revista Matemática Iberoamericana

We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.

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