Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces

@article{Antonelli2019PaulsRA,
  title={Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces},
  author={Gioacchino Antonelli and Enrico Le Donne},
  journal={arXiv: Metric Geometry},
  year={2019}
}
This paper is related to the problem of finding a good notion of rectifiability in sub-Riemannian geometry. In particular, we study which kind of results can be expected for smooth hypersurfaces in Carnot groups. Our main contribution will be a consequence of the following result: there exists a $C^{\infty}$ hypersurface $S$ without characteristic points that has uncountably many pairwise non-isomorphic tangent groups on every positive-measure subset. The example is found in a Carnot group of… Expand