Left-invariant optimal control problems on Lie groups are an important class of problems
with a large symmetry group. They are theoretically interesting because they can often be …

Nonholonomic systems are control systems which depend linearly on the control. Their
underlying geometry is the sub-Riemannian geometry, which plays for these systems the …

Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups
equipped with a path distance that is invariant by left-translations of the group and admit …

This book concerns a fresh development of the eternal idea of the distance as the length of a
shortest path. In Euclidean geometry, shortest paths are segments of straight lines that …

These notes aim at illustrating some results achieved in the geometric measure theory in
Carnot groups. They are an extended version of a part of the course Geometric Measure …

We give the complete classification of left-invariant sub-Riemannian structures on three
dimensional Lie groups in terms of the basic differential invariants. This classifications …

We prove that ideal sub-Riemannian manifolds (ie, admitting no non-trivial abnormal
minimizers) support interpolation inequalities for optimal transport. A key role is played by …

Nous établissons le développement asymptotique en temps petit de noyaux de la chaleur d’opérateurs
de Hörmander hypoelliptiques au voisinage de la diagonale, généralisant des résultats …

For an equiregular sub-Riemannian manifold M, Popp's volume is a smooth volume which is
canonically associated with the sub-Riemannian structure, and it is a natural generalization …

Исследование инвариантных управляемых систем на группах Ли и однородных
пространствах является одной из центральных тем геометрической теории …