Overview of the Geometries of Shape Spaces and Diffeomorphism GroupsReport as inadecuate



 Overview of the Geometries of Shape Spaces and Diffeomorphism Groups


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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.



Author: Martin Bauer; Martins Bruveris; Peter W. Michor

Source: https://archive.org/



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