The chapter reviews geometric constructions for averages, subdivision, and multiresolution transforms on metric spaces, Riemannian manifolds, and groups, with emphasis on convergence and smoothness results.
Barycentric coordinate neighbourhoods in Riemannian manifolds
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abstract
We quantify conditions that ensure that a signed measure on a Riemannian manifold has a well defined centre of mass. We then use this result to quantify the extent of a neighbourhood on which the Riemannian barycentric coordinates of a set of $n+1$ points on an $n$-manifold provide a true coordinate chart, i.e., the barycentric coordinates provide a diffeomorphism between a neighbourhood of a Euclidean simplex, and a neighbourhood containing the points on the manifold.
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math.NA 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Geometric subdivision and multiscale transforms
The chapter reviews geometric constructions for averages, subdivision, and multiresolution transforms on metric spaces, Riemannian manifolds, and groups, with emphasis on convergence and smoothness results.