The Bj\"orling problem amounts to the construction of a minimal surface from a real-analytic curve with a given real-analytic normal vector field. We approximate that solution locally by discrete minimal surfaces as special discrete isothermic surfaces (as defined by Bobenko and Pinkall in 1996). The main step in our construction is the approximation of the sought surface's Weierstrass data by discrete conformal maps. We prove that the approximation error is of the order of the square of the mesh size.

翻译：Björling问题涉及从给定实解析法向量场的实解析曲线构造极小曲面。我们通过离散极小曲面（即Bobenko与Pinkall于1996年定义的特殊离散等温曲面）对该解进行局部逼近。构造的核心步骤是用离散共形映射逼近所求曲面的Weierstrass数据。我们证明逼近误差的量级为网格尺寸的平方阶。