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On the structure of finite perimeter sets in step 2 Carnot groups

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Abstract

In this article we study codimension 1 rectifiable sets in Carnot groups and we extend classical De Giorgi ’s rectifiability and divergence theorems to the setting of step 2 groups. Related problems in higher step Carnot groups are discussed, pointing on new phenomena related to the blow up procedure.

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Correspondence to Bruno Franchi.

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First author was supported by University of Bologna, Italy, funds for selected research topics; second and third authors were supported by MURST, Italy, and University of Trento, Italy.

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Franchi, B., Serapioni, R. & Cassano, F.S. On the structure of finite perimeter sets in step 2 Carnot groups. J Geom Anal 13, 421–466 (2003). https://doi.org/10.1007/BF02922053

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