On Completeness of Groups of Diffeomorphisms
By Martins Bruveris, Franccois-Xavier Vialard. 2014
83 citations recorded by the source corpus.
We study completeness properties of the Sobolev diffeomorphism groups $\mathcal D^s(M)$ endowed with strong right-invariant Riemannian metrics when the underlying manifold $M$ is $\mathbb R^d$ or compact without boundary. The main result is that for $s > \dim M/2 + 1$, the group $\mathcal D^s(M)$ is geodesically and metrically complete with a surjective exponential map. We then present the connection between the Sobolev diffeomorphism group and the large deformation matching framework in order to apply our results to diffeomorphic image matching.
Subfields: Computational Mechanics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5524a10d82699e8164e82d789247f3d904119891
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In Geometry and Topology
- Peter W. Michor
- Martins Bruveris
- David Mumford
- B. Clarke
- Tamás Hausel
- Richard M. Murray
- Andrea Censi
In Mathematical Physics
Citations in the corpus
- GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES (2013, background): “have also been studied on the diffeomorphism group in [6].”