Rectifiability of Sets of Finite Perimeter in a class of Carnot Groups of arbitrary step

Details Rectifiability of Sets of Finite Perimeter in a class of Carnot Groups of arbitrary step Rectifiability of Sets of Finite Perimeter in a class of Carnot Groups of arbitrary step

2012-01-16

arxiv.org/abs/1201.3277v1

Mathematics

Classical Analysis and ODEs

Scientific paper

In this Note, we define a class of Carnot groups of arbitrary step (that are called "groups of type $\star$" throughout the paper), and we prove that the reduced boundary of a set of finite intrinsic perimeter in a group of type $\star$ is rectifiable in the intrinsic sense (De Giorgi's rectifiability theorem). This result extends previous results proved by Franchi, Serapioni & Serra Cassano in step 2 groups.

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