Lecturer:
Course Type:
PhD Course
Academic Year:
2014-2015
Period:
January-April
Duration:
60 h
Description:
1. Isoperimetric problem and Heisenberg group.
2. Sub-Riemannian length and metric.
3. Rashevskii-Chow theorem.
4. Existence of length-minimizers.
5. Normal and abnormal geodesics.
6. Hamiltonian setting; Hamiltonian characterization of geodesics.
7. The endpoint map and the exponential map; conjugate and cut points.
8. Nonholonomic tangent space.
9. Popp volume and Hausdorff measure.
10. Sub-Laplacian and sub-Riemannian heat equation.
11. Lie groups and left-invariant sub-Riemannian structures.
12. Low-dimensional models.
13. Analytic properties of the Carnot-Caratheodory distance.
14. Second variation and Jacobi curves.
15. Sub-Riemannian curvature.
Research Group:
Location:
A-133