Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/15764
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dc.contributor.authorBauer, M-
dc.contributor.authorBruveris, M-
dc.contributor.authorKolev, B-
dc.date.accessioned2018-02-01T14:19:44Z-
dc.date.available2018-02-01T14:19:44Z-
dc.date.issued2017-
dc.identifier.citationCalculus of Variations and Partial Differential Equationsen_US
dc.identifier.issnhttp://arxiv.org/abs/1703.03323v1-
dc.identifier.issn0944-2669-
dc.identifier.issn1432-0835-
dc.identifier.urihttp://bura.brunel.ac.uk/handle/2438/15764-
dc.description.abstractMotivated 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 𝑑 ) and on its Sobolev completions ℐ π‘ž (S1 , R 𝑑 ). We prove local well-posedness of the geodesic equations both on the Banach manifold ℐ π‘ž (S1 , R 𝑑 ) and on the FrΒ΄echetmanifold Imm(S1 , R 𝑑 ) provided the order of the metric is greater or equal to one. In addition we show that the 𝐻𝑠 -metric induces a strong Riemannian metric on the Banach manifold ℐ 𝑠 (S1 , R 𝑑 ) of the same order 𝑠, provided 𝑠 > 3 2 . These investigations can be also interpreted as a generalization of the analysis for right invariant metrics on the diffeomorphism group.en_US
dc.language.isoenen_US
dc.publisherSPRINGER VERLAGen_US
dc.subjectSobolev metrics of fractional orderen_US
dc.titleFractional Sobolev Metrics on Spaces of Immersed Curvesen_US
dc.typeArticleen_US
dc.identifier.doihttp://dx.doi.org/10.1007/s00526-018-1300-7-
dc.relation.isPartOfCalculus of Variations and Partial Differential Equations-
pubs.publication-statusAccepted-
Appears in Collections:Dept of Mathematics Research Papers

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