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arXiv · 1606.01585

Barycentric coordinate neighbourhoods in Riemannian manifolds

Ramsay Dyer·Gert Vegter·Mathijs Wintraecken
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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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Ramsay Dyer, Gert Vegter, Mathijs Wintraecken. 2016-06-05. Barycentric coordinate neighbourhoods in Riemannian manifolds. https://arxiv.org/abs/1606.01585

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