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On a variety of algebraic minimal surfaces in Euclidean 4-space. (English) Zbl 0958.53008
The author proves that the moduli space of the Weierstrass data for algebraic minimal surfaces in Euclidean 4-space with fixed topological type, orders of branch points and ends, and total curvature, has the structure of a real analytic variety. The author further gives lower bounds of its dimension. The author also shows that the moduli space of the Weierstrass data for stable algebraic minimal surfaces in Euclidean 4-space has the structure of a complex analytic variety.

MSC:
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
58D27 Moduli problems for differential geometric structures
58E12 Variational problems concerning minimal surfaces (problems in two independent variables)
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