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http://bura.brunel.ac.uk/handle/2438/9561
Title: | Geodesic Completeness for Sobolev Metrics on the Space of Immersed Plane Curves |
Authors: | Bruveris, M Michor, PW Mumford, D |
Keywords: | 2010 Mathematics Subject Classification: 58D15 (primary);35G55, 53A04, 58B20 (secondary) |
Issue Date: | 2014 |
Publisher: | Forum of Mathematics |
Citation: | Forum of Mathematics, Sigma, 1 (e19), 2014 |
Abstract: | We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2 and higher is globally well-posed for smooth initial data as well as initial data in certain Sobolev spaces. Thus the space of closed plane curves equipped with such a metric is geodesically complete. We find lower bounds for the geodesic distance in terms of curvature and its derivatives. |
URI: | http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9307773&fileId=S205050941400019X http://bura.brunel.ac.uk/handle/2438/9561 |
DOI: | http://dx.doi.org/10.1017/fms.2014.19 |
ISSN: | 2050-5094 |
Appears in Collections: | Dept of Mathematics Research Papers |
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