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Introduction to sub-Riemannian geometry

Lecturer: 
Course Type: 
PhD Course
Academic Year: 
2018-2019
Period: 
March - May
Duration: 
40 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.
Location: 
A-133

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