In differential geometry, the Chen–Gackstatter surface family (or the Chen–Gackstatter–Thayer surface family) is a family of minimal surfaces that generalize the Enneper surface by adding handles, giving it nonzero topological genus.
They are not embedded, and have Enneper-like ends. The members formula_1 of the family are indexed by the number of extra handles "i" and the winding number of the Enneper end; the total genus is "ij" and the total Gaussian curvature is formula_2. It has been shown that formula_3 is the only genus one orientable complete minimal surface of total curvature formula_4.
It has been conjectured that continuing to add handles to the surfaces will in the limit converge to the Scherk's second surface (for "j" = 1) or the saddle tower family for "j"  ; 1.
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