Discrete constant mean curvature surfaces on general graphs

• DOI: 10.1007/s10711-022-00733-3
• Publication Date: 2022-09-29T04:02:41Z
• Authors: Tim Hoffmann; Shimpei Kobayashi; Zi Ye
• Keywords: Constant (computer programming); Constant-mean-curvature surface; Zero (linguistics); Constant curvature; Minimal surface; Representation; Discrete group

Abstract The contribution of this paper is twofold. First, we generalize the definition discrete isothermic surfaces. Compared with previous ones, it covers more surfaces, e.g., associated families minimal and non-zero constant mean curvature (CMC in short) whose counterpart smooth case are Second, show that CMC surfaces can be obtained by holomorphic data (a solution additive rational Toda system) via generalized Weierstrass type representation.