The article discusses the construction of minimal surfaces from real analytic curves with given normal vector fields, focusing on solving the Björling problem locally through discrete minimal surfaces. The main approach involves choosing suitable data from real-analytic functions to determine initial values for discrete holomorphic functions and eventually obtain discrete minimal surfaces. The process ensures existence and convergence of the discrete minimal surfaces, approximating the smooth solution of the Björling problem. Various mathematical concepts such as Weierstrass representation, conformal maps, and cross-ratios are utilized in this construction.
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arxiv.org
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