Corpus ID: 221995963

On rectifiable measures in Carnot groups: structure theory

@article{Antonelli2020OnRM,
  title={On rectifiable measures in Carnot groups: structure theory},
  author={Gioacchino Antonelli and Andrea Merlo},
  journal={arXiv: Metric Geometry},
  year={2020}
}
In this paper we prove the one-dimensional Preiss' theorem in the first Heisenberg group $\mathbb H^1$. More precisely we show that a Radon measure $\phi$ on $\mathbb H^1$ with positive and finite one-density with respect to the Koranyi distance is supported on a one-rectifiable set in the sense of Federer, i.e., it is supported on the countable union of the images of Lipschitz maps $A\subseteq \mathbb R\to\mathbb H^1$. The previous theorem is a consequence of a Marstrand-Mattila type… Expand
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References

SHOWING 1-10 OF 45 REFERENCES
A rectifiability result for finite-perimeter sets in Carnot groups
On uniform measures in the Heisenberg group.
Characteristic points, rectifiability and perimeter measure on stratified groups
Metric Lie groups admitting dilations.
Lipschitz graphs and currents in Heisenberg groups
Intrinsically Lipschitz functions with normal target in Carnot groups
Regular Hypersurfaces, Intrinsic Perimeter and Implicit Function Theorem in Carnot Groups
TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS
  • V. Magnani
  • Mathematics
  • Journal of the Australian Mathematical Society
  • 2013
...
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2
3
4
5
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