Construction of continuum from a discrete surface by its iterated subdivisions
Differential Geometry
2022-03-31 v4
Abstract
Given a trivalent graph in the 3-dimensional Euclidean space, we call it a discrete surface because it has a tangent space at each vertex determined by its neighbor vertices. To abstract a continuum object hidden in the discrete surface, we introduce a subdivision method by applying the Goldberg-Coxeter subdivision and discuss the convergence of a sequence of discrete surfaces defined inductively by the subdivision. We also study the limit set as the continuum geometric object associated with the given discrete surface.
Cite
@article{arxiv.1806.03531,
title = {Construction of continuum from a discrete surface by its iterated subdivisions},
author = {Motoko Kotani and Hisashi Naito and Chen Tao},
journal= {arXiv preprint arXiv:1806.03531},
year = {2022}
}
Comments
22 pages, 10 figures and 2 tables