Discrete constant mean curvature cylinders and isothermic tori

2024/01/12 by Cho, Joseph, Leschke, Katrin, Ogata, Yuta
#(2020): 53A70 (Primary) 53A10 #53A31 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.06570

Abstract

We consider the monodromy problem of Darboux transforms of discrete isothermic surfaces using the integrable theory of discrete polarised curves. Then we provide, for the first time, closed-form discrete parametrisations of discrete isothermic cylinders, discrete constant mean curvature cylinders, and discrete isothermic tori.

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