Local conditions for triangulating submanifolds of Euclidean space
Résumé
In this paper, we consider the following setting: suppose that we are given a manifold in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is they are homeomorphic.
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