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| Riemannian metrics on the space of curves are used in shape analysis to describe deformations that take one shape to another and to define a distance between shapes. The talk will focus on a particular class of metrics, metrics of Sobolev type. They arose from the need of strengthen the $L^2$-metric, which was found to have vanishing geodesic distance. I will describe recent work on the geodesic and metric completeness of Soblev metrics on the space of plane curves. |
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