Barycentric coordinate neighbourhoods in Riemannian manifolds

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.

References in corpus (1)

• Riemannian Center of Mass and so called karcher mean

Cited by in corpus (2)

• Five Degree-of-Freedom Property Interpolation of Arbitrary Grain Boundaries via Voronoi Fundamental Zone Octonion Framework
• Distortion estimates for barycentric coordinates on Riemannian simplices