Transvectant - Revision history

en>BG19bot: /* Definition */WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: ^{th → ^th using AWB (9957)}

2014-03-01T08:53:18Z

Definition: WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: th → th using AWB (9957)

← Older revision		Revision as of 10:53, 1 March 2014
Line 1:		Line 1:
	~~In [[mathematics]]~~, the ''~~'measurable Riemann mapping theorem'''~~ is a ~~theorem proved in 1960 by [[Lars Ahlfors]]~~ and ~~[[Lipman Bers]] in [[complex analysis]]~~ and ~~[[geometric function theory]]~~. ~~Contrary~~ to ~~its name~~, it is not a ~~direct generalization~~ of the ~~[[Riemann mapping theorem]]~~, ~~but instead a result concerning [[quasiconformal mapping]]s~~ and ~~solutions of~~ the ~~[[Beltrami equation]]~~. ~~The result was prefigured by earlier results of [[Charles Morrey]] from 1938 on quasi-linear [[elliptic partial differential equation]]s~~.		The COOLEST is a transportable party disguised as a cooler, bringing blended drinks, music and exciting to any outdoor occasion. On the water, in particular in the hot summer season, a good cooler is essential. This places them in an awkward position as far as the market is concerned for the reason that they expense 3 occasions as considerably for only a modest acquire in overall performance. For the price you're almost certainly be much better off spending even extra and going with a greater-end efficiency cooler if you genuinely need to have the enhanced insulation. Popular Mechanics' Andy Hill outlines the complete method of converting a cooler into a tun utilizing a round cooler, not our Coleman.<br><br><br><br>It really is a noisy planet and your content material should be syndicated across the social web to drive awareness and engagement. A wine refrigerator or cooler should be employed to retailer ready-to-drink wines at their proper serving temperatures, not age wine for ten years. Vinotemp, a wine cooler manufacturer states that it really is typical for the temperature in its compressor-based models to fluctuate +/- 5°F. Most wine coolers do not handle humidity, normally their relative humidity is 40%.<br><br>I've heard of outfitters that will retailer their high performance coolers in a walk in commercial freezer ahead of use. When prepared to go, they load the coolers full of cold meals, pack in thermal blankets or other insulation to take up any space around the meals, then close and latch the cooler. They then seal about the cooler lid with duct tape to maintain cold in and individuals out. There are wine coolers that are made with a constructed in wine rack. The world of transportable coolers is a complex 1.<br><br>At this stage, these utilized huge blocks of ice to cool it. But this meant they had been massive, heavy and cumbersome. A water cooler unit standard of the period could only be moved by several people today at after. And coolers are inexpensive and are readily out there. Most schools, offices and hospitals have installed water coolers. Bottleless the water coolers is connected straight to the water provide pipe and has a filtering process that purifies water.<br><br>Igloo drink coolers are mainly made to keep beverages cold. The only two coolers approved by Igloo to hold hot beverages are the Igloo beverage cube with the friction-match lid and the classic stainless steal coolers. Don't forget that the Igloo coolers are not created to heat a beverage, they just sustain the temperature of the beverage at the time it is poured into the cooler. Very carefully pour the beverage into your cooler safeguarding oneself from splashes.<br><br>Carolina Coolers is a division of Filters Rapidly Nearby Service at situated in Monroe. Eric Coolers Preserve Ice Days Helms, a single of New York City's true juicing pioneers, co-founded Healing Cooler immediately after seeing his prospects respond to the restorative power of juices. Motorcycle oil coolers are critical to the life of all motorcycle engines. Best Wine Coolers provides details about the organization and supplies quick to use get in touch with info.<br><br>Pack into your cooler and it acts as an ice block that won&39t melt all more than your food! When you loved this informative article and you want to receive more information regarding [http://www.bestcoolerreviewshq.com/best-coolers-for-keeping-ice/ greatest coolers for maintaining ice] i implore you to visit the internet site. Locate coleman 12 volt cooler facts and discount rates with our large choice. Applying the Coleman Energy Chill Iceless 12-Volt Cooler can make the difference in between getting warm drinks and completely chilled treats. Our 12v coolers and warmers by Coleman are engineered to meet all of your outdoor dining requires. Select from soft-sided or sturdy really hard-sided coolers.<br><br>In other words, the cooler is the very same, but there are four of them :) Let's see what the new Phanteks offspring is capable of and if it will be able to outperform the Thermalright cooler. So the people at Yeti have applied their knowledge at keeping meals and drinks cold to a soft-sided cooler bag which can be squeezed into the tightest spots. Tailgating includes several inebriated people today crowding around tiny coolers and grills.<br><br>In order to differentiate between decrease-finish and greater-end models, Igloo and Coleman (among other folks) have adopted a technique of naming and advertising and marketing their coolers right after the length of time they can maintain one thing cold. It relies on draining and weighing the quantity of meltwater developed at regular measurement told us the percentage of ice that had melted up to that point in time. In liquids, hotter regions are much less dense than cooler places.

	The ~~theorem~~ of ~~Alhfors and Bers states that if μ~~ is a ~~bounded measurable function on '''C''' with~~ <~~math~~>~~\\|\mu\\|_\infty < 1~~<~~/math~~>, ~~then~~ there is a
	~~unique solution ''f'' of the Beltrami equation~~

	:<~~math~~> ~~\partial_{\overline{z}} f(z) = \mu(z) \partial_z f(z)~~<~~/math~~>

	~~for which~~ '~~'f'' is~~ a ~~quasiconformal homeomorphism~~ of ~~'''C''' fixing~~ the ~~points 0, 1 and ∞. A similar result~~ is ~~true with '''C''' replaced by~~ the ~~[[unit disk]] '''D'''~~. ~~Their proof used~~ the ~~[[Beurling transform]]~~, a ~~[[singular integral operator]].~~
	~~==References==~~
	*{{citation\|first=Lars\|last=Ahfors\|first2=Lipman\|last2=Bers\|title=Riemann mapping's ~~theorem for variable metrics\|journal= Annals~~ of ~~Math~~.~~\|volume= 72\|year=1960\|pages= 385–404}}~~
	*{{citation\|last=Ahlfors\|first=Lars V.~~\|authorlink=Lars Ahlfors\|title=Lectures on quasiconformal mappings\|publisher=Van Nostrand\|year=1966}}~~
	*{{citation\|title=Elliptic partial differential equations and ~~quasiconformal mappings~~ in ~~the plane\|volume= 48\|series= Princeton mathematical series\|~~
	~~first=Kari\|last= Astala\|first2= Tadeusz \|last2=Iwaniec\|first3= Gaven\|last3= Martin\|publisher=Princeton University Press\|year= 2009\|~~
	~~isbn=0-691-13777-3\|pages=161–172}}~~
	*{{citation\|last=Carleson\|first=L.~~\|last2= Gamelin\|first2= T~~. D. ~~W.\|title=Complex dynamics\|series=~~
	~~Universitext: Tracts in Mathematics\|publisher= Springer~~-~~Verlag\|year=1993\|isbn=0~~-~~387~~-~~97942~~-~~5}}~~
	*{{citation
	~~\| title = On~~ the ~~solutions of quasi~~-~~linear elliptic partial differential equations~~
	~~\| first = Charles B~~. Jr.
	~~\| last = Morrey~~
	~~\| authorlink = Charles B~~. ~~Morrey~~, ~~Jr.~~
	~~\| journal = [[Transactions~~ of the ~~American Mathematical Society]]~~
	~~\| volume = 43~~
	~~\| year = 1938~~
	~~\| pages = 126–166~~
	~~\| doi = 10~~.~~2307/1989904~~
	~~\| issue = 1~~
	~~\| jstor = 1989904~~
	~~\| jfm = 62~~.~~0565~~.02
	~~\| mr = 1501936~~
	~~\| zbl = 0018~~.~~40501~~
	}}
	*{{citation\|title=When ellipses look like circles: the ~~measurable Riemann mapping theorem\|first=Saeed\|last=Zakeri\|first2=Mahmood\|last2=Zeinalian\|url=http://www~~.~~math.qc.edu/~zakeri/papers/ahl-bers~~.~~pdf\|journal=Nashr-e-Riazi\|volume= 8 \|year=1996\|pages=5–14}}~~

	~~[[Category:Theorems in complex analysis]]~~

	~~{{mathanalysis-stub}}~~

en>Gene Ward Smith at 03:38, 29 September 2012

2012-09-29T03:38:52Z

← Older revision		Revision as of 05:38, 29 September 2012
Line 1:		Line 1:
	~~For functions of this article~~, ~~let’s outline what I imply by pocket knife. Obviously it~~ is a ~~knife that's meant to be carried~~ in ~~your pocket. More particularly nonetheless, I'm defining a pocket knife as a folding knife~~ and ~~as such I will probably be neglecting fastened blade knives~~ and ~~multitools, as they are outside the scope of this article~~ [~~http://www.thebestpocketknifereviews.com/the-best-survival-knife-top-rated-wild-knives-in-the-world/ Best Fixed Blade Survival Knife Your Opinion~~]. ~~At 7.8 ounces~~, ~~the ZT 0200~~ is a ~~beast. I recommend this knife for~~ a ~~survival folder or for general use round~~ the ~~home~~. The ~~scale makes is cumbersome to hold day~~ by ~~day, to not point out the blade length makes it unlawful to hold in lots~~ of ~~locales~~.~~<br><br>~~The ~~general fit~~ of ~~this knife is superb, I would rate it at ninety eight% or higher. The fit between the cocobolo scales~~ and ~~the stainless-steel liners and SS bolsters~~ is ~~one hundred% with no gaps and completely clean transitions. There are just~~ a ~~few hairlines between the bolsters and the liners which under no circumstances detracts from the standard, as they~~'~~re solely noticeable when in comparison~~ with ~~other elements where the fit~~ is ~~so tight they appear to be one piece. I like the size. Having~~ a ~~bit extra blade and a deal with that fills the palm~~ of ~~your hand actually makes~~ the ~~knife extra useful in that "device" way.~~<br><br>~~The College~~ of ~~York researchers discovered that after two years~~, ~~Infuse supplied no clinically important pain reduction~~ and ~~was related to a doable elevated danger of cancer, although again,~~ the ~~general threat was low~~. ~~The~~ [~~https://Li442-134~~.~~members~~.~~linode~~.~~com/u/nozbd/ findings recommend] that Infuse should be used primarily~~ in ~~its place for sufferers who otherwise would require multiple incision to reap their very own bone for grafting on~~ the ~~surgical procedure web site, in line with an editorial by [http://c2687710~~.~~Myzen~~.co.~~uk/groups/solingen~~-~~wilderness~~-~~survival~~-~~knife/ Dr Daniel] Resnick of~~ the ~~University~~ of ~~Wisconsin and Dr Kevin Bozic of the University of California, San Francisco~~.~~<br><br>Pocket knives have been a necessary appliance for numerous uses, over quite a few generations~~. ~~It's simply thoughts boggling at how lengthy this utility instrument has been a viable selection because the “go to” gadget for a myriad of people over time~~. ~~Civilization after civilization have made use of the pocketknife~~, ~~creating various types~~ of ~~modifications along~~ the ~~best way, all the while, still maintaining the [http:~~/~~/esmikorea~~.~~ezconn~~.~~net/xe/?document_srl~~=~~87038 identical basic] operate~~. ~~The recognition of~~ the pocket knife has led to the big success of the preferred manufacturers in circulation at this time. Origins What in case your knife budget is simply the money you found in your automobile’s ashtray and underneath the sofa cushions?<br><br>The CKTACBSD Knife has serrated edges on the [http://~~Istoriya~~.~~sumy~~.~~ua/index~~.~~php~~/Schrade_Schf9_Extreme_Survival_Knife_Review underside portion] of the knife to cut by rope and rope, and I must say that the factors on these have been really pretty sharp. I still sharpen them up a bit but to be sincere they didn't really need it. I examined the development of the pocket knife and located that there was no play or motion when wiggling the [http://~~Perloca~~.com/The_Best_Full_Tang_Survival_Knife blade round] so it at all times stays in place while it is open. I don't really feel just like the knife will break or go flying out when I flick it open or close it.<br><br>Most of us purchase Boker Plus Anti-Grav Knife swiss military knife for above talked about causes and although there is no such thing as a single cutlery that can accomplish all of the work recommendations out that a lot of makes making cutlery that can assist all of us on many of the duties. Switzerland Military Knives are the very best Boker Plus Anti-Grav Knife so we highly suggest getting their products since they provides several tools that can fulfil our personal all requirement and emerged at cheap worth, these individuals price each penny of the money. article elaborates in ~~much larger detail on utilizing the data in our review to seek out the very best blade for your functions.~~		In [[mathematics]], the '''measurable Riemann mapping theorem''' is a theorem proved in 1960 by [[Lars Ahlfors]] and [[Lipman Bers]] in [[complex analysis]] and [[geometric function theory]]. Contrary to its name, it is not a direct generalization of the [[Riemann mapping theorem]], but instead a result concerning [[quasiconformal mapping]]s and solutions of the [[Beltrami equation]]. The result was prefigured by earlier results of [[Charles Morrey]] from 1938 on quasi-linear [[elliptic partial differential equation]]s.

			The theorem of Alhfors and Bers states that if μ is a bounded measurable function on '''C''' with <math>\\|\mu\\|_\infty < 1</math>, then there is a
			unique solution ''f'' of the Beltrami equation

			:<math> \partial_{\overline{z}} f(z) = \mu(z) \partial_z f(z)</math>

			for which ''f'' is a quasiconformal homeomorphism of '''C''' fixing the points 0, 1 and ∞. A similar result is true with '''C''' replaced by the [[unit disk]] '''D'''. Their proof used the [[Beurling transform]], a [[singular integral operator]].
			==References==
			*{{citation\|first=Lars\|last=Ahfors\|first2=Lipman\|last2=Bers\|title=Riemann mapping's theorem for variable metrics\|journal= Annals of Math.\|volume= 72\|year=1960\|pages= 385–404}}
			*{{citation\|last=Ahlfors\|first=Lars V.\|authorlink=Lars Ahlfors\|title=Lectures on quasiconformal mappings\|publisher=Van Nostrand\|year=1966}}
			*{{citation\|title=Elliptic partial differential equations and quasiconformal mappings in the plane\|volume= 48\|series= Princeton mathematical series\|
			first=Kari\|last= Astala\|first2= Tadeusz \|last2=Iwaniec\|first3= Gaven\|last3= Martin\|publisher=Princeton University Press\|year= 2009\|
			isbn=0-691-13777-3\|pages=161–172}}
			*{{citation\|last=Carleson\|first=L.\|last2= Gamelin\|first2= T. D. W.\|title=Complex dynamics\|series=
			Universitext: Tracts in Mathematics\|publisher= Springer-Verlag\|year=1993\|isbn=0-387-97942-5}}
			*{{citation
			\| title = On the solutions of quasi-linear elliptic partial differential equations
			\| first = Charles B. Jr.
			\| last = Morrey
			\| authorlink = Charles B. Morrey, Jr.
			\| journal = [[Transactions of the American Mathematical Society]]
			\| volume = 43
			\| year = 1938
			\| pages = 126–166
			\| doi = 10.2307/1989904
			\| issue = 1
			\| jstor = 1989904
			\| jfm = 62.0565.02
			\| mr = 1501936
			\| zbl = 0018.40501
			}}
			*{{citation\|title=When ellipses look like circles: the measurable Riemann mapping theorem\|first=Saeed\|last=Zakeri\|first2=Mahmood\|last2=Zeinalian\|url=http://www.math.qc.edu/~zakeri/papers/ahl-bers.pdf\|journal=Nashr-e-Riazi\|volume= 8 \|year=1996\|pages=5–14}}

			[[Category:Theorems in complex analysis]]

			{{mathanalysis-stub}}

en>Headbomb: Various citation cleanup (identifiers mostly), replaced: | url=http://dx.doi.org/10.1006/aama.2000.0700 → | doi=10.1006/aama.2000.0700, | id={{MR|1783553}} → | mr=1783553, typos fixed: , → ,, added Empty section (1) t using AWB

2011-09-02T03:43:45Z

Various citation cleanup (identifiers mostly), replaced: | url=http://dx.doi.org/10.1006/aama.2000.0700 → | doi=10.1006/aama.2000.0700, | id={{MR|1783553}} → | mr=1783553, typos fixed: , → ,, added Empty section (1) t using AWB

New page

For functions of this article, let’s outline what I imply by pocket knife. Obviously it is a knife that's meant to be carried in your pocket. More particularly nonetheless, I'm defining a pocket knife as a folding knife and as such I will probably be neglecting fastened blade knives and multitools, as they are outside the scope of this article [http://www.thebestpocketknifereviews.com/the-best-survival-knife-top-rated-wild-knives-in-the-world/ Best Fixed Blade Survival Knife Your Opinion]. At 7.8 ounces, the ZT 0200 is a beast. I recommend this knife for a survival folder or for general use round the home. The scale makes is cumbersome to hold day by day, to not point out the blade length makes it unlawful to hold in lots of locales. The general fit of this knife is superb, I would rate it at ninety eight% or higher. The fit between the cocobolo scales and the stainless-steel liners and SS bolsters is one hundred% with no gaps and completely clean transitions. There are just a few hairlines between the bolsters and the liners which under no circumstances detracts from the standard, as they're solely noticeable when in comparison with other elements where the fit is so tight they appear to be one piece. I like the size. Having a bit extra blade and a deal with that fills the palm of your hand actually makes the knife extra useful in that "device" way. The College of York researchers discovered that after two years, Infuse supplied no clinically important pain reduction and was related to a doable elevated danger of cancer, although again, the general threat was low. The [https://Li442-134.members.linode.com/u/nozbd/ findings recommend] that Infuse should be used primarily in its place for sufferers who otherwise would require multiple incision to reap their very own bone for grafting on the surgical procedure web site, in line with an editorial by [http://c2687710.Myzen.co.uk/groups/solingen-wilderness-survival-knife/ Dr Daniel] Resnick of the University of Wisconsin and Dr Kevin Bozic of the University of California, San Francisco. Pocket knives have been a necessary appliance for numerous uses, over quite a few generations. It's simply thoughts boggling at how lengthy this utility instrument has been a viable selection because the “go to” gadget for a myriad of people over time. Civilization after civilization have made use of the pocketknife, creating various types of modifications along the best way, all the while, still maintaining the [http://esmikorea.ezconn.net/xe/?document_srl=87038 identical basic] operate. The recognition of the pocket knife has led to the big success of the preferred manufacturers in circulation at this time. Origins What in case your knife budget is simply the money you found in your automobile’s ashtray and underneath the sofa cushions? The CKTACBSD Knife has serrated edges on the [http://Istoriya.sumy.ua/index.php/Schrade_Schf9_Extreme_Survival_Knife_Review underside portion] of the knife to cut by rope and rope, and I must say that the factors on these have been really pretty sharp. I still sharpen them up a bit but to be sincere they didn't really need it. I examined the development of the pocket knife and located that there was no play or motion when wiggling the [http://Perloca.com/The_Best_Full_Tang_Survival_Knife blade round] so it at all times stays in place while it is open. I don't really feel just like the knife will break or go flying out when I flick it open or close it. Most of us purchase Boker Plus Anti-Grav Knife swiss military knife for above talked about causes and although there is no such thing as a single cutlery that can accomplish all of the work recommendations out that a lot of makes making cutlery that can assist all of us on many of the duties. Switzerland Military Knives are the very best Boker Plus Anti-Grav Knife so we highly suggest getting their products since they provides several tools that can fulfil our personal all requirement and emerged at cheap worth, these individuals price each penny of the money. article elaborates in much larger detail on utilizing the data in our review to seek out the very best blade for your functions.

← Older revision		Revision as of 10:53, 1 March 2014
Line 1:		Line 1:
	~~In [[mathematics]]~~, the ''~~'measurable Riemann mapping theorem'''~~ is a ~~theorem proved in 1960 by [[Lars Ahlfors]]~~ and ~~[[Lipman Bers]] in [[complex analysis]]~~ and ~~[[geometric function theory]]~~. ~~Contrary~~ to ~~its name~~, it is not a ~~direct generalization~~ of the ~~[[Riemann mapping theorem]]~~, ~~but instead a result concerning [[quasiconformal mapping]]s~~ and ~~solutions of~~ the ~~[[Beltrami equation]]~~. ~~The result was prefigured by earlier results of [[Charles Morrey]] from 1938 on quasi-linear [[elliptic partial differential equation]]s~~.		The COOLEST is a transportable party disguised as a cooler, bringing blended drinks, music and exciting to any outdoor occasion. On the water, in particular in the hot summer season, a good cooler is essential. This places them in an awkward position as far as the market is concerned for the reason that they expense 3 occasions as considerably for only a modest acquire in overall performance. For the price you're almost certainly be much better off spending even extra and going with a greater-end efficiency cooler if you genuinely need to have the enhanced insulation. Popular Mechanics' Andy Hill outlines the complete method of converting a cooler into a tun utilizing a round cooler, not our Coleman.<br><br><br><br>It really is a noisy planet and your content material should be syndicated across the social web to drive awareness and engagement. A wine refrigerator or cooler should be employed to retailer ready-to-drink wines at their proper serving temperatures, not age wine for ten years. Vinotemp, a wine cooler manufacturer states that it really is typical for the temperature in its compressor-based models to fluctuate +/- 5°F. Most wine coolers do not handle humidity, normally their relative humidity is 40%.<br><br>I've heard of outfitters that will retailer their high performance coolers in a walk in commercial freezer ahead of use. When prepared to go, they load the coolers full of cold meals, pack in thermal blankets or other insulation to take up any space around the meals, then close and latch the cooler. They then seal about the cooler lid with duct tape to maintain cold in and individuals out. There are wine coolers that are made with a constructed in wine rack. The world of transportable coolers is a complex 1.<br><br>At this stage, these utilized huge blocks of ice to cool it. But this meant they had been massive, heavy and cumbersome. A water cooler unit standard of the period could only be moved by several people today at after. And coolers are inexpensive and are readily out there. Most schools, offices and hospitals have installed water coolers. Bottleless the water coolers is connected straight to the water provide pipe and has a filtering process that purifies water.<br><br>Igloo drink coolers are mainly made to keep beverages cold. The only two coolers approved by Igloo to hold hot beverages are the Igloo beverage cube with the friction-match lid and the classic stainless steal coolers. Don't forget that the Igloo coolers are not created to heat a beverage, they just sustain the temperature of the beverage at the time it is poured into the cooler. Very carefully pour the beverage into your cooler safeguarding oneself from splashes.<br><br>Carolina Coolers is a division of Filters Rapidly Nearby Service at situated in Monroe. Eric Coolers Preserve Ice Days Helms, a single of New York City's true juicing pioneers, co-founded Healing Cooler immediately after seeing his prospects respond to the restorative power of juices. Motorcycle oil coolers are critical to the life of all motorcycle engines. Best Wine Coolers provides details about the organization and supplies quick to use get in touch with info.<br><br>Pack into your cooler and it acts as an ice block that won&39t melt all more than your food! When you loved this informative article and you want to receive more information regarding [http://www.bestcoolerreviewshq.com/best-coolers-for-keeping-ice/ greatest coolers for maintaining ice] i implore you to visit the internet site. Locate coleman 12 volt cooler facts and discount rates with our large choice. Applying the Coleman Energy Chill Iceless 12-Volt Cooler can make the difference in between getting warm drinks and completely chilled treats. Our 12v coolers and warmers by Coleman are engineered to meet all of your outdoor dining requires. Select from soft-sided or sturdy really hard-sided coolers.<br><br>In other words, the cooler is the very same, but there are four of them :) Let's see what the new Phanteks offspring is capable of and if it will be able to outperform the Thermalright cooler. So the people at Yeti have applied their knowledge at keeping meals and drinks cold to a soft-sided cooler bag which can be squeezed into the tightest spots. Tailgating includes several inebriated people today crowding around tiny coolers and grills.<br><br>In order to differentiate between decrease-finish and greater-end models, Igloo and Coleman (among other folks) have adopted a technique of naming and advertising and marketing their coolers right after the length of time they can maintain one thing cold. It relies on draining and weighing the quantity of meltwater developed at regular measurement told us the percentage of ice that had melted up to that point in time. In liquids, hotter regions are much less dense than cooler places.

	The ~~theorem~~ of ~~Alhfors and Bers states that if μ~~ is a ~~bounded measurable function on '''C''' with~~ <~~math~~>~~\\|\mu\\|_\infty < 1~~<~~/math~~>, ~~then~~ there is a
	~~unique solution ''f'' of the Beltrami equation~~

	:<~~math~~> ~~\partial_{\overline{z}} f(z) = \mu(z) \partial_z f(z)~~<~~/math~~>

	~~for which~~ '~~'f'' is~~ a ~~quasiconformal homeomorphism~~ of ~~'''C''' fixing~~ the ~~points 0, 1 and ∞. A similar result~~ is ~~true with '''C''' replaced by~~ the ~~[[unit disk]] '''D'''~~. ~~Their proof used~~ the ~~[[Beurling transform]]~~, a ~~[[singular integral operator]].~~
	~~==References==~~
	*{{citation\|first=Lars\|last=Ahfors\|first2=Lipman\|last2=Bers\|title=Riemann mapping's ~~theorem for variable metrics\|journal= Annals~~ of ~~Math~~.~~\|volume= 72\|year=1960\|pages= 385–404}}~~
	*{{citation\|last=Ahlfors\|first=Lars V.~~\|authorlink=Lars Ahlfors\|title=Lectures on quasiconformal mappings\|publisher=Van Nostrand\|year=1966}}~~
	*{{citation\|title=Elliptic partial differential equations and ~~quasiconformal mappings~~ in ~~the plane\|volume= 48\|series= Princeton mathematical series\|~~
	~~first=Kari\|last= Astala\|first2= Tadeusz \|last2=Iwaniec\|first3= Gaven\|last3= Martin\|publisher=Princeton University Press\|year= 2009\|~~
	~~isbn=0-691-13777-3\|pages=161–172}}~~
	*{{citation\|last=Carleson\|first=L.~~\|last2= Gamelin\|first2= T~~. D. ~~W.\|title=Complex dynamics\|series=~~
	~~Universitext: Tracts in Mathematics\|publisher= Springer~~-~~Verlag\|year=1993\|isbn=0~~-~~387~~-~~97942~~-~~5}}~~
	*{{citation
	~~\| title = On~~ the ~~solutions of quasi~~-~~linear elliptic partial differential equations~~
	~~\| first = Charles B~~. Jr.
	~~\| last = Morrey~~
	~~\| authorlink = Charles B~~. ~~Morrey~~, ~~Jr.~~
	~~\| journal = [[Transactions~~ of the ~~American Mathematical Society]]~~
	~~\| volume = 43~~
	~~\| year = 1938~~
	~~\| pages = 126–166~~
	~~\| doi = 10~~.~~2307/1989904~~
	~~\| issue = 1~~
	~~\| jstor = 1989904~~
	~~\| jfm = 62~~.~~0565~~.02
	~~\| mr = 1501936~~
	~~\| zbl = 0018~~.~~40501~~
	}}
	*{{citation\|title=When ellipses look like circles: the ~~measurable Riemann mapping theorem\|first=Saeed\|last=Zakeri\|first2=Mahmood\|last2=Zeinalian\|url=http://www~~.~~math.qc.edu/~zakeri/papers/ahl-bers~~.~~pdf\|journal=Nashr-e-Riazi\|volume= 8 \|year=1996\|pages=5–14}}~~

	~~[[Category:Theorems in complex analysis]]~~

	~~{{mathanalysis-stub}}~~

Transvectant - Revision history

en>BG19bot: /* Definition */WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: th → th using AWB (9957)

en>Gene Ward Smith at 03:38, 29 September 2012

en>Headbomb: Various citation cleanup (identifiers mostly), replaced: | url=http://dx.doi.org/10.1006/aama.2000.0700 → | doi=10.1006/aama.2000.0700, | id={{MR|1783553}} → | mr=1783553, typos fixed: , → ,, added Empty section (1) t using AWB

en>BG19bot: /* Definition */WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: ^{th → ^th using AWB (9957)}