Costa's minimal surface
In mathematics, Costa's minimal 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. Topologically, it is a thrice-punctured torus.
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. Its discovery triggered research and discovery into several new surfaces and open conjectures in topology.
The Costa surface can be described using the Weierstrass zeta and the Weierstrass elliptic functions.
References
- Lua error in package.lua at line 80: module 'strict' not found. Ph.D. Thesis, IMPA, Rio de Janeiro, Brazil.
- Lua error in package.lua at line 80: module 'strict' not found. Bol. Soc. Bras. Mat. 15, 47–54.
- Lua error in package.lua at line 80: module 'strict' not found. From MathWorld--A Wolfram Web Resource.
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