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dc.contributor.authorBruveris, M-
dc.contributor.authorMøller-Andersen, J-
dc.identifier.citationarXiv:1705.07976v1 [math.DG]-
dc.description.abstractIn this article we prove completeness results for Sobolev metrics with nonconstant coefficients on the space of immersed curves and on the space of unparametrized curves. We provide necessary as well as sufficient conditions for the coefficients of the Riemannian metric for the metric to be metrically complete and we construct examples of incomplete metrics. This work is an extension of previous work on completeness of Sobolev metrics with constant coefficients.en_US
dc.publisherCornell University-
dc.subjectimmersed curvesen_US
dc.subjectSobolev metricsen_US
dc.subjectminimizing geodesicsen_US
dc.subjectshape spaceen_US
dc.titleCompleteness of Length-Weighted Sobolev Metrics on the Space of Curvesen_US
pubs.notes15 pages, 1 figure-
Appears in Collections:Dept of Mathematics Research Papers

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