Completeness and Geodesic Distance Properties for Fractional Sobolev Metrics on Spaces of Immersed Curves
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We investigate the geometry of the space of immersed closed curves equipped with reparametrization-invariant Riemannian metrics; the metrics we consider are Sobolev metrics of possible fractional-order q∈[0,∞). We establish the critical Sobolev ind... ...
