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http://bura.brunel.ac.uk/handle/2438/10067
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DC Field | Value | Language |
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dc.contributor.author | Bruveris, M | - |
dc.date.accessioned | 2015-02-03T10:12:21Z | - |
dc.date.available | 2014-07-02 | - |
dc.date.available | 2015-02-03T10:12:21Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | 2014 | en_US |
dc.identifier.uri | http://arxiv.org/abs/1407.0601v1 | - |
dc.identifier.uri | http://bura.brunel.ac.uk/handle/2438/10067 | - |
dc.description.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. | en_US |
dc.language.iso | en | en_US |
dc.subject | math.DG | en_US |
dc.subject | math.DG | en_US |
dc.subject | 58D10 (primary), 58D20, 53A04, 35A01 (secondary) | en_US |
dc.title | Completeness properties of Sobolev metrics on the space of curves | en_US |
dc.type | Article | en_US |
pubs.notes | 24 pages | - |
pubs.notes | 24 pages | - |
pubs.organisational-data | /Brunel | - |
pubs.organisational-data | /Brunel/Brunel Staff by College/Department/Division | - |
pubs.organisational-data | /Brunel/Brunel Staff by College/Department/Division/College of Engineering, Design and Physical Sciences | - |
pubs.organisational-data | /Brunel/Brunel Staff by College/Department/Division/College of Engineering, Design and Physical Sciences/Dept of Mathematics | - |
pubs.organisational-data | /Brunel/Brunel Staff by College/Department/Division/College of Engineering, Design and Physical Sciences/Dept of Mathematics/Mathematical Sciences | - |
Appears in Collections: | Dept of Mathematics Research Papers |
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Fulltext.pdf | 436.2 kB | Unknown | View/Open |
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