Divided power structure - Revision history

en>David Eppstein: /* References */ link Arthur Ogus

2014-11-20T03:15:50Z

References: link Arthur Ogus

← Older revision		Revision as of 05:15, 20 November 2014
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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]]]]		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.<br><br>Feel free to visit my web site ... tarot card readings [[http://www.january-yjm.com/xe/index.php?mid=video&document_srl=158289 http://www.january-yjm.com/]]

	~~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}}~~

en>Mdd: Correction(s)

2013-09-10T13:33:23Z

Correction(s)

← Older revision		Revision as of 15:33, 10 September 2013
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	~~The author~~'s ~~title~~ is ~~Christy Brookins~~. ~~To perform lacross~~ is ~~the factor I adore most~~ of ~~all~~. ~~For~~ a ~~whilst I've been in Alaska but I will have~~ to ~~transfer in~~ a ~~yr or two~~. ~~Invoicing~~ is ~~my occupation~~.<br><br>~~My site; psychic love readings ([http://www~~.~~herandkingscounty~~.~~com~~/~~content/information-~~and~~-facts-you-must-know-about-hobbies~~ http://~~www~~.~~herandkingscounty~~.com/~~content/information~~-~~and~~-~~facts~~-~~you~~-~~must-know-about~~-~~hobbies])~~		[[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}}

67.134.207.224: /* Definition */

2011-10-26T17:37:11Z

Definition

New page

The author's title is Christy Brookins. To perform lacross is the factor I adore most of all. For a whilst I've been in Alaska but I will have to transfer in a yr or two. Invoicing is my occupation.<br><br>My site; psychic love readings ([http://www.herandkingscounty.com/content/information-and-facts-you-must-know-about-hobbies http://www.herandkingscounty.com/content/information-and-facts-you-must-know-about-hobbies])