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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.
ISSN: 2050-5094
Appears in Collections:Dept of Mathematics Research Papers

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