@article{06a855dffbca4f64858f4eafc3c66d6a,
title = "CONSTRUCTION OF CONTINUUM FROM A DISCRETE SURFACE BY ITS ITERATED SUBDIVISIONS",
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 subdivisionmethod 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.",
keywords = "convergence theory, discrete curvature, Discrete geometry",
author = "Motoko Kotani and Hisashi Naito and Chen Tao",
note = "Funding Information: 2010 Mathematics Subject Classification. Primary 52C99, Secondary 53A05, 53C23, 65D17. Key words and phrases. Discrete geometry, discrete curvature, convergence theory. Authors (KM and HN) were partially supported by JSPS KAKENHI Grants Numbers JP17H06465, JP17H06466, and JP19K03488. KM was partially supported by JST, CREST Grant Number JPMJCR17J4, Japan. Publisher Copyright: {\textcopyright} 2022 Tohoku University, Mathematical Institute. All rights reserved.",
year = "2022",
doi = "10.2748/tmj.20201225",
language = "English",
volume = "74",
pages = "229--252",
journal = "Tohoku Mathematical Journal",
issn = "0040-8735",
publisher = "Tohoku University, Mathematical Institute",
number = "2",
}