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http://bura.brunel.ac.uk/handle/2438/10742
Title: | On Completeness of Groups of Diffeomorphisms |
Authors: | Bruveris, M Vialard, FX |
Keywords: | Diffeomorphism groups;Sobolev metrics;strong Riemannian metric;completeness;minimizing geodesics |
Issue Date: | 2014 |
Publisher: | Cornell University |
Citation: | arXiv:1403.2089v4 [math.DG] |
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: | https://bura.brunel.ac.uk/handle/2438/10742 https://arxiv.org/abs/1403.2089v4 |
Appears in Collections: | Dept of Mathematics Research Papers |
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