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This paper extends parts of the results from [17] for plane curves to the case of hypersurfaces in R n. Let M be a compact connected oriented n − 1 dimensional manifold without boundary like S 2 or the torus S 1 × S 1. Then shape space is either the manifold of submanifolds of R n of type M , or the orbifold of immersions from M to R n modulo the group of(More)
ii iii In nova fert animus mutatas dicere formas corpora; di, coeptis (nam vos mutastis et illas) adspirate meis primaque ab origine mundi ad mea perpetuum deducite tempora carmen! * The persistence of memory by Salvador Dali. Picture taken from Abstract. Many procedures in science, engineering and medicine produce data in the form of geometric shapes.(More)
We study Sobolev-type metrics of fractional order on the group of compactly supported diffeomorphisms Diffc(M), where M is a Riemannian manifold of bounded geometry. We prove that the geodesic distance, induced by the Riemannian metric, vanishes if the order s satisfies 0 ≤ s < 1 2. For M = R we show the vanishing of the geodesic distance also for s = 1 2 ,(More)
Let M be a compact connected oriented n−1 dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from M to R n. The results of [1], where mean curvature weighted metrics were studied, suggest to incorporate Gauß curvature weights in the definition of the metric. This leads us to study metrics on shape(More)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings,(More)
On the manifold M(M) of all Riemannian metrics on a compact manifold M one can consider the natural L 2-metric as decribed first by [10]. In this paper we consider variants of this metric which in general are of higher order. We derive the geodesic equations, we show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic(More)