Bruno Franchi, Dipartimento di Matematica, Universita di Bologna, Piazza di porta San Donato, 5, 40126 Bologna, Italy, e-mail: franchib@dm.unibo.it; Raul Serapioni, Dipartimento di Matematica, Universita di Trento, Via Sommarive 14, 38050, Povo (Trento) Italy, e-mail: serapion@science.unitn.it; Francesco Serra Cassano, Dipartimento di Matematica, Universita di Trento, Via Sommarive 14, 38050, Povo (Trento) Italy, e-mail: cassano@science.unitn.it
Abstract: We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi's theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these results, comments and an exhaustive bibliography can be found in our preprint (2001).
Keywords: Carnot groups, perimeter, rectifiability, divergence theorem
Classification (MSC 2000): 49Q15, 22E30
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