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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]]]]
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| 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]].
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| 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.
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| The Costa surface can be described using the [[Weierstrass zeta function|Weierstrass zeta]] and the [[Weierstrass elliptic function|Weierstrass elliptic]] [[function (mathematics)|functions]].
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| ==References==
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| * {{cite book
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| | author = Costa, Celso José da
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| | title = Imersões mínimas completas em <math>\mathbb{R}^3</math> de gênero um e curvatura total finita
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| | year = 1982
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| }} ''Ph.D. Thesis, IMPA, Rio de Janeiro, Brazil.''
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| * {{cite book
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| | author = Costa, Celso José da
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| | title = Example of a complete minimal immersion in <math>\mathbb{R}^3</math> of genus one and three embedded ends
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| | year = 1984
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| }} ''Bol. Soc. Bras. Mat. 15, 47–54.''
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| * {{cite web
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| | author = Weisstein, Eric W.
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| | title = Costa Minimal Surface.
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| | url=http://mathworld.wolfram.com/CostaMinimalSurface.html
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| | accessdate=2006-11-19
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| }} ''From MathWorld--A Wolfram Web Resource.''
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| [[Category:Differential geometry]]
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| [[Category:Minimal surfaces]]
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| {{topology-stub}}
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The author's title is Christy. To climb is something I really appreciate performing. Distributing manufacturing has been his profession for some time. My spouse and I reside in Kentucky.
Feel free to visit my web site ... tarot card readings [http://www.january-yjm.com/]