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|Title:||Geodesic Completeness for Sobolev Metrics on the Space of Immersed Plane Curves|
|Keywords:||2010 Mathematics Subject Classification: 58D15 (primary);35G55, 53A04, 58B20 (secondary)|
|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.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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