Construction of Discrete Minimal Surfaces and their Properties Kemal Aziez Rachmansyah
Mathematical Institute, Graduate School of Science, Tohoku University
Abstract
In this work, we aim to survey recent advances in discrete minimal surface
theories and compare them. Each approach is independent to each other and comes with different properties. The approaches discussed are Konrad Polthier^s work in [1] that took advantage of the area-minimizing property of a minimal surface, Wai Yeung Lam^s work in [2] that constructs two types of minimal surfaces, and Kotani, Naito, and Omori^s work in [3] where they defined the discrete analogue of fundamental forms. Each approach has its own discrete version of Weierstrass representation.
References
[1] A. I. Bobenko, T. Hoffman, and A. B. Springborn, Minimal surfaces from circle patterns: Geometry from combinatorics, Annals of Mathematics 164 (2006), 231-264.
[2] W. Y. Lam, Discrete Minimal Surfaces, Critical Points of the Area Functional from Integrable Systems, International Mathematics Research Notices 2018, no. 6, 1808-1845.
[3] M. Kotani, H. Naito, and T. Omori, A discrete surface theory, Computer Aided Geometric Design 58 (2017), 24-54.
