Lecturer:
Course Type:
PhD Course
Academic Year:
2018-2019
Period:
March - May
Duration:
40 h
Description:
- Isoperimetric problem and Heisenberg group.
- Sub-Riemannian length and metric.
- Rashevskii-Chow theorem.
- Existence of length-minimizers.
- Normal and abnormal geodesics.
- Hamiltonian setting; Hamiltonian characterization of geodesics.
- The endpoint map and the exponential map; conjugate and cut points.
- Nonholonomic tangent space.
- Popp volume and Hausdorff measure.
- Sub-Laplacian and sub-Riemannian heat equation.
- Lie groups and left-invariant sub-Riemannian structures.
- Low-dimensional models.
- Analytic properties of the Carnot-Caratheodory distance.
- Second variation and Jacobi curves.
- Sub-Riemannian curvature.
Location:
A-133