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[[File:Costa's minimal surface (200x150).ogv|thumbtime=0 |thumb |200px |alt=Computer rendering of Costa's minimal surface.|Costa's minimal surface, cropped by a sphere. [[:File:Costa's minimal surface.ogv|Higher resolution video]]]] | |||
In [[mathematics]], '''Costa's minimal surface''' is an embedded [[minimal surface]] discovered in 1982 by the [[Brazil]]ian [[mathematician]] [[Celso José da Costa]]. It is also a surface of finite topology, which means that it can be formed by puncturing a [[compact space|compact]] surface. Topologically, it is a thrice-punctured [[torus]]. | |||
Until its discovery, the [[plane (geometry)|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 (topology)|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 function|Weierstrass zeta]] and the [[Weierstrass elliptic function|Weierstrass elliptic]] [[function (mathematics)|functions]]. | |||
==References== | |||
* {{cite book | |||
| author = Costa, Celso José da | |||
| title = Imersões mínimas completas em <math>\mathbb{R}^3</math> de gênero um e curvatura total finita | |||
| year = 1982 | |||
}} ''Ph.D. Thesis, IMPA, Rio de Janeiro, Brazil.'' | |||
* {{cite book | |||
| author = Costa, Celso José da | |||
| title = Example of a complete minimal immersion in <math>\mathbb{R}^3</math> of genus one and three embedded ends | |||
| year = 1984 | |||
}} ''Bol. Soc. Bras. Mat. 15, 47–54.'' | |||
* {{cite web | |||
| author = Weisstein, Eric W. | |||
| title = Costa Minimal Surface. | |||
| url=http://mathworld.wolfram.com/CostaMinimalSurface.html | |||
| accessdate=2006-11-19 | |||
}} ''From MathWorld--A Wolfram Web Resource.'' | |||
[[Category:Differential geometry]] | |||
[[Category:Minimal surfaces]] | |||
{{topology-stub}} | |||
Revision as of 15:33, 10 September 2013
File:Costa's minimal surface (200x150).ogv
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
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Ph.D. Thesis, IMPA, Rio de Janeiro, Brazil. - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Bol. Soc. Bras. Mat. 15, 47–54. - Template:Cite web From MathWorld--A Wolfram Web Resource.