On Completeness of Groups of Diffeomorphisms
Differential Geometry
2016-01-28 v4 Analysis of PDEs
Abstract
We study completeness properties of the Sobolev diffeomorphism groups endowed with strong right-invariant Riemannian metrics when the underlying manifold is or compact without boundary. The main result is that for , the group 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 to apply our results to diffeomorphic image matching.
Keywords
Cite
@article{arxiv.1403.2089,
title = {On Completeness of Groups of Diffeomorphisms},
author = {Martins Bruveris and François-Xavier Vialard},
journal= {arXiv preprint arXiv:1403.2089},
year = {2016}
}
Comments
43 pages, revised version