Skew minimal surfaces supported by two triangular frames

M. M. Alimov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2022), pp. 3-25.

Résumé

We use the Chaplygin hodograph transformation to explicitly solve the problem of finding skew minimal surfaces supported by two triangular equilateral frames. The skew arises due to the special position of the frames: they are not coaxial but have central symmetry about a certain point, and mirror symmetry about one of the three planes formed by pairs of parallel bisectors of the upper and lower frames. In the particular case of coaxial frames, we compare our solution with the solution of the problem obtained by the Weierstrass–Enneper method.

Détail

Keywords: minimal surface
Mots-clés : hodograph transformation, complex variable.

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