Costa's minimal surface

In mathematics, Costa's minimal surface or Costa's surface, is an embedded minimal surface discovered in 1982 by the Brazilian mathematician Celso José da Costa.

It is also a surface of finite topology, which means that it can be formed by puncturing a compact surface.

Until its discovery, the plane, helicoid and the catenoid were believed to be the only embedded minimal surfaces that could be formed by puncturing a compact surface.

The Costa surface evolves from a torus, which is deformed until the planar end becomes catenoidal.

Defining these surfaces on rectangular tori of arbitrary dimensions yields the Costa surface.