Sub-Riemannian geometry on the group of motions of the plane
Yuri Sachkov and Andrei Ardentov (Pereslavl)
Abstract: We will discuss the unique, up to local isometries, contact sub-Riemannian structure on the group SE(2) of proper motions of the plane (aka group of rototranslations). The following questions will be addressed: - geodesics, - their local and global optimality, - cut time, cut locus, and spheres, - infinite geodesics, - bicycle transform and relation of geodesics with Euler elasticae, - group of isometries and homogeneous geodesics, - applications to imaging and robotics.
analysis of PDEsdifferential geometrymetric geometryoptimization and controlspectral theory
Audience: researchers in the topic
Series comments: The "Sub-Riemannian seminars" are the union of the "Séminaire de géométrie et analyse sous-riemannienne" (held in Paris since 2011) and the "International Sub-Riemannian Seminars", which were born in spring 2020 as a reaction to the COVID-19 pandemic.
The new format will gather every 3 weeks on average, alternating between these types of sessions:
- physical session in Paris (Laboratoire Jacques-Louis Lions), also transmitted online on Zoom.
- fully online session on Zoom.
- special session hosted physically somewhere else, and transmitted online.
| Organizers: | Ugo Boscain, Enrico Le Donne, Luca Rizzi*, Mario Sigalotti, Emmanuel Trelat |
| *contact for this listing |