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Problems of Mathematical Control Theory
May 22, 2015 15:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina)
 


Sub-Riemannian minimizers, spheres, and cut loci

Yu. L. Sachkov

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Abstract: 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.

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