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research article
Overview of the Geometries of Shape Spaces and Diffeomorphism Groups
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics that can be defined thereon, and what is known about the properties of these metrics. We put particular emphasis on the induced geodesic distance, the geodesic equation and its well-posedness, geodesic and metric completeness and properties of the curvature.
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Name
10851_2013_Article_490.pdf
Type
Publisher's version
Access type
openaccess
Size
1.65 MB
Format
Adobe PDF
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c024d3f5c321b48b0f17eb4252161f7f