Special Session 16: Optimal control and its applications
Contents
We will give estimates for the number of conjugate points along
extremals of a general sub-Riemannian metric in terms of curvature-type
invariants of this metric. These estimates generalize the classical Rauch
and Bonnet-Myers comparison theorems in Riemannian Geometry and they are
based on the differential geometry of curves in Lagrangian Grassmannians
developed in my previous works with Chengbo Li. The special emphasis will
be given to the case of sub-Riemannian metrics on distributions of rank 2
where the formulation of the comparison theorems is especially simple.