Sets with constant normal in Carnot groups: properties and examples

@article{Bellettini2019SetsWC,
  title={Sets with constant normal in Carnot groups: properties and examples},
  author={Costante Bellettini and Enrico Le Donne},
  journal={arXiv: Differential Geometry},
  year={2019}
}
We analyze subsets of Carnot groups that have intrinsic constant normal, as they appear in the blowup study of sets that have finite sub-Riemannian perimeter. The purpose of this paper is threefold. First, we prove some mild regularity and structural results in arbitrary Carnot groups. Namely, we show that for every constant-normal set in a Carnot group its sub-Riemannian-Lebesgue representative is regularly open, contractible, and its topological boundary coincides with the reduced boundary… Expand
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