Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/10067
 Title: Completeness properties of Sobolev metrics on the space of curves Authors: Bruveris, M Keywords: math.DG;math.DG;58D10 (primary), 58D20, 53A04, 35A01 (secondary) Issue Date: 2014 Citation: 2014 Abstract: We study completeness properties of Sobolev metrics on the space of immersed curves and on the shape space of unparametrized curves. We show that Sobolev metrics of order $n\geq 2$ are metrically complete on the space $\mathcal I^n(S^1,\mathbb R^d)$ of Sobolev immersions of the same regularity and that any two curves in the same connected component can be joined by a minimizing geodesic. These results then imply that the shape space of unparametrized curves has the structure of a complete length space. URI: http://arxiv.org/abs/1407.0601v1http://bura.brunel.ac.uk/handle/2438/10067 Appears in Collections: Dept of Mathematics Research Papers

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