The symmetrized Costa surface with two catenoidal ends and one planar end was first described by David Hoffman and William Meeks in 1990.

In retrospect, this generalization looks like a small step. As for the Costa surface, there is not really a period problem to solve besides adjusting the López-Ros factor, and the embeddedness proof is not more difficult, either.

However, these were the first embedded minimal surfaces of finite total curvature of arbitrarily large genus, and thus opened a door into completely new terrain.

Moreover, images of the surface with high genus have the appearance of a catenoid intersected by a plane and desingularized by a bent singly periodic Scherk surface. This has triggered the groundbreaking work of Nikos Kapouleas on gluing constructions and led to research that is still ongoing.

##### Resources

D. Hoffman and W. H. Meeks: *Embedded minimal surfaces of finite topology*. Annals of Mathematics **131** (1990), 1–34.

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