Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/10742
 Title: On Completeness of Groups of Diffeomorphisms Authors: Bruveris, MVialard, FX Keywords: math.DG;58D05, 58B20;math.AP Issue Date: 2014 Publisher: arXiv.org Citation: 2014 Abstract: 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 also extend the result to its closed subgroups, in particular the group of volume preserving diffeomorphisms and the group of symplectomorphisms. 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. URI: http://bura.brunel.ac.uk/handle/2438/10742 ISSN: http://arxiv.org/abs/1403.2089v2 Appears in Collections: Publications

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