Tohoku Mathematical Journal
2022
June
SECOND SERIES VOL. 74, NO. 2

Tohoku Math. J.
74 (2022), 215-227

Title CONSTRUCTION OF CONTINUUM FROM A DISCRETE SURFACE BY ITS ITERATED SUBDIVISIONS

Author Motoko Kotani, Hisashi Naito and Chen Tao

(Received May 12, 2020, revised December 21, 2020)
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.

Mathematics Subject Classification. Primary 52C99, Secondary 53A05, 53C23, 65D17.
Key words and phrases. Discrete geometry, discrete curvature, convergence theory.

To the top of this page

Back to the Contents