Sub-Riemannian minimizers, spheres, and cut loci

The talk will be devoted to the following issues.
General results on sub-Riemannian minimizers and spheres:
- existence of minimizers,
- Pontryagin maximum principle, normal and abnormal geodesics,
- cut points, Maxwell points, conjugate points,
- regularity of spheres.
Method of computation of cut time and cut locus via analysis of symmetries of the exponential mapping and the corresponding Maxwell points.
Left-invariant sub-Riemannian problems on Lie groups with complete or partial description of minimizers, spheres and cut loci:
- Heisenberg group,
- group of Euclidean motions of the plane SE(2),
- group of hyperbolic motions of the plane SH(2),
- Engel group.