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http://bura.brunel.ac.uk/handle/2438/15764
Title: | Fractional Sobolev Metrics on Spaces of Immersed Curves |
Authors: | Bauer, M Bruveris, M Kolev, B |
Keywords: | Sobolev metrics of fractional order |
Issue Date: | 2017 |
Publisher: | Springer-Verlag |
Citation: | Calculus of Variations and Partial Differential Equations, 2018, 57(1):27 (24 pp.) |
Abstract: | Motivated by applications in the field of shape analysis, we study reparametrization invariant, fractional order Sobolev-type metrics on the space of smooth regular curves Imm(S1 , R π ) and on its Sobolev completions β π (S1 , R π ). We prove local well-posedness of the geodesic equations both on the Banach manifold β π (S1 , R π ) and on the FrΒ΄echetmanifold Imm(S1 , R π ) provided the order of the metric is greater or equal to one. In addition we show that the π»π -metric induces a strong Riemannian metric on the Banach manifold β π (S1 , R π ) of the same order π , provided π > 3 2 . These investigations can be also interpreted as a generalization of the analysis for right invariant metrics on the diffeomorphism group. |
URI: | https://bura.brunel.ac.uk/handle/2438/15764 https://arxiv.org/abs/1703.03323v1 |
DOI: | https://doi.org/10.1007/s00526-018-1300-7 |
ISSN: | 0944-2669 |
Appears in Collections: | Dept of Mathematics Research Papers |
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