Chaplygin’s hodograph method of classical fluid mechanics is applied to explicitly solve the Plateau problem of finding minimal surfaces. The minimal surfaces are formed between two mirror-symmetric polygonal frames having a common axis of symmetry. Two classes of minimal surfaces are found: the class of regular surfaces continuously connecting the supporting frames forming a tube with complex shape; and the class of singular surfaces which have a partitioning film closing the tube in between. As an illustration of the general solution, minimal surfaces supported by triangular frames are fully described. The theory is experimentally validated using soap films. The general solution is compared with the known particular solutions obtained by the Weierstrass inverse method.

中文翻译：

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镜像对称框架上的最小表面：流体动力学类比

Chaplygin's hodograph 经典流体力学方法用于明确解决寻找极小曲面的高原问题。最小表面形成在具有公共对称轴的两个镜像对称多边形框架之间。发现了两类极小曲面：一类是连续连接支撑框架形成复杂形状管的规则面；以及具有将管子封闭在其间的分隔膜的奇异表面类。作为一般解决方案的说明，三角形框架支持的最小表面被完整描述。该理论使用肥皂膜进行了实验验证。将通解与通过 Weierstrass 逆方法获得的已知特解进行比较。