Corpus ID: 235829187

Cut time in the sub-Riemannian problem on the Cartan group

@inproceedings{Ardentov2021CutTI,
  title={Cut time in the sub-Riemannian problem on the Cartan group},
  author={Andrei Andreevich Ardentov and Eero Hakavuori},
  year={2021}
}
We study the sub-Riemannian structure determined by a left-invariant distribution of rank 2 on a step 3 Carnot group of dimension 5. We prove the conjectured cut times of Y. Sachkov for the sub-Riemannian Cartan problem. Along the proof, we obtain a comparison with the known cut times in the sub-Riemannian Engel group, and a sufficient (generic) condition for the uniqueness of the length minimizer between two points. Hence we reduce the optimal synthesis to solving a certain system of equations… 
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TLDR
To the knowledge, this is the first explicit computation of the whole cut locus in sub-Riemannian geometry, except for the trivial case of the Heisenberg group.
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