On Completeness of Groups of Diffeomorphisms

@article{Bruveris2014OnCO,
  title={On Completeness of Groups of Diffeomorphisms},
  author={Martins Bruveris and Franccois-Xavier Vialard},
  journal={arXiv: Differential Geometry},
  year={2014}
}
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… 
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