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 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 . It has been shown that is the only genus one orientable complete minimal surface of total curvature ..
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.
References
External links The Chen–Gackstatter Thayer Surfaces at the Scientific Graphics Project Chen–Gackstatter Surface in the Minimal Surface Archive Xah Lee's page on Chen–Gackstatter