Completeness properties of diffeomorphism groups
Event details
| Date | 18.03.2014 |
| Hour | 16:15 › 17:15 |
| Speaker | Martins Bruveris (EPFL) |
| Location |
MA A3 31
|
| Category | Conferences - Seminars |
Geometry and Dynamics Seminar
Abstract: Motivated by the development of diffeomorphic image matching, I will describe strong Riemannian metrics on the group of Sobolev diffeomorphisms. This group is a Hilbert manifold and a topological group, but not a Lie group. Nevertheless it admits smooth strong right-invariant Riemannian metrics. By studying regularity and continuity properties of the flow map, one can show that the group is both metrically complete and admits minimizing geodesics between any two diffeomorphisms. I will show, how these results relate to the variational methods used in the large deformation matching framework.
Abstract: Motivated by the development of diffeomorphic image matching, I will describe strong Riemannian metrics on the group of Sobolev diffeomorphisms. This group is a Hilbert manifold and a topological group, but not a Lie group. Nevertheless it admits smooth strong right-invariant Riemannian metrics. By studying regularity and continuity properties of the flow map, one can show that the group is both metrically complete and admits minimizing geodesics between any two diffeomorphisms. I will show, how these results relate to the variational methods used in the large deformation matching framework.
Practical information
- Expert
- Free
Organizer
- Martins Bruveris, Sonja Hohloch, Marc Troyanov