Please use this identifier to cite or link to this item:
http://bura.brunel.ac.uk/handle/2438/10742
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Bruveris, M | - |
dc.contributor.author | Vialard, FX | - |
dc.date.accessioned | 2015-05-06T08:56:20Z | - |
dc.date.available | 2014-03-09 | - |
dc.date.available | 2015-05-06T08:56:20Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | arXiv:1403.2089v4 [math.DG] | en_US |
dc.identifier.uri | https://bura.brunel.ac.uk/handle/2438/10742 | - |
dc.identifier.uri | https://arxiv.org/abs/1403.2089v4 | - |
dc.description.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. | en_US |
dc.language.iso | en | en_US |
dc.publisher | Cornell University | en_US |
dc.subject | Diffeomorphism groups | en_US |
dc.subject | Sobolev metrics | en_US |
dc.subject | strong Riemannian metric | en_US |
dc.subject | completeness | - |
dc.subject | minimizing geodesics | - |
dc.title | On Completeness of Groups of Diffeomorphisms | en_US |
dc.type | Preprint | en_US |
pubs.notes | 31 pages, expanded introduction and corrected typos | - |
Appears in Collections: | Dept of Mathematics Research Papers |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
FullText.pdf | 383.93 kB | Adobe PDF | View/Open |
Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.