Geodesic
On completeness of groups of diffeomorphisms
Journal of the European Mathematical Society, Tome 19 (2017) no. 5, pp. 1507-1544 Cet article a éte moissonné depuis la source EMS Press

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We study completeness properties of the Sobolev diffeomorphism groups Ds(M) endowed with strong right-invariant Riemannian metrics when M is Rd or a compact manifold without boundary. We prove that for s> dim (M)/2+1, the group Ds(M) is geodesically and metrically complete and any two diffeomorphisms in the same component can be joined by a minimal geodesic. 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.
DOI : 10.4171/jems/698
Classification : 58-XX, 35-XX
Keywords: Diffeomorphism groups, Sobolev metrics, strong Riemannian metric, completeness, minimizing geodesics 
@article{JEMS_2017_19_5_a5,
     author = {Martins Bruveris and Fran\c{c}ois-Xavier Vialard},
     title = {On completeness of groups of diffeomorphisms},
     journal = {Journal of the European Mathematical Society},
     pages = {1507--1544},
     year = {2017},
     volume = {19},
     number = {5},
     doi = {10.4171/jems/698},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/698/}
}
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Martins Bruveris; François-Xavier Vialard. On completeness of groups of diffeomorphisms. Journal of the European Mathematical Society, Tome 19 (2017) no. 5, pp. 1507-1544. doi: 10.4171/jems/698

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