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Topic: Bieberbach conjecture

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	PlanetMath: Bieberbach's conjecture (Site not responding. Last check: 2007-10-08)
		The following theorem is known as the Bieberbach conjecture, even though it has now been proven.
		Bieberbach proposed it in 1916 and it was finally proven in 1984 by Louis de Branges.
		This is version 4 of Bieberbach's conjecture, born on 2004-06-07, modified 2006-09-17.
	planetmath.org /encyclopedia/BieberbachsConjecture.html (108 words)

	Bieberbach biography (Site not responding. Last check: 2007-10-08)
		Bieberbach was appointed professor of mathematics in Basel in Switzerland, Frankfurt am Main in Germany, and the University of Berlin where he held the chair of geometry.
		Bieberbach was managing editor of the Jahresbericht der Deutschen Mathematiker-Vereinigung in 1934 and he published an "open letter" in the journal which was highly critical of Harald Bohr because he had attacked Bieberbach's racist views.
		Ostrowski respected Bieberbach's contribution as a mathematician, and considered his political views were irrelevant in his remarkable contributions to mathematics.
	www-groups.dcs.st-and.ac.uk /history/Biographies/Bieberbach.html (898 words)

	De Branges' theorem - Wikipedia, the free encyclopedia
		In complex analysis, a branch of mathematics, de Branges' theorem, named after Louis de Branges, formerly called the Bieberbach conjecture, after Ludwig Bieberbach, states a necessary condition on a holomorphic function to map the open unit disk of the complex plane injectively to the complex plane.
		The case n = 1 of De Branges' theorem is essentially the Schwarz lemma, which was known in the nineteenth century and is a consequence of the maximum modulus principle, applied to f(z)/z.
		The conjecture was stated in 1916 by Bieberbach, after having proved the case n=2.
	en.wikipedia.org /wiki/Bieberbach_conjecture (391 words)

	Bieberbach conjecture
		A celebrated conjecture made by the German mathematician Ludwig Bieberbach (1886-1982) in 1916, which was finally proved, after many partial results by others, by Louis de Branges of Purdue University in 1984.[54] Bierberbach is infamous in the history of mathematics because of his outspoken anti-Semitism during the Nazi era.
		Following the dismissal of Edmund Landau (1877-1938) from the University of Göttingen, Bierberbach wrote: “This should be seen as a prime example of the fact that representatives of overly different races do not mix as students and teachers...
		Bieberbach’s conjecture (BC) stemmed from the Riemann conjecture (RC), which makes a claim about any region of a plane that is simply-connected (in other words, any region, however complicated, that doesn't have any holes).
	www.daviddarling.info /encyclopedia/B/Bieberbach_conjecture.html (369 words)

	Bieberbach
		Ludwig Bieberbach was Professor of Mathematics in Berlin and did important work on function theory.
		Bieberbach had a reputation as an inspiring but rather disorganised teacher.
		Bieberbach also studied polynomials (1914), now named after him, which approximate a function that conformally maps a given simply-connected domain onto a disc.
	members.tripod.com /sfabel/mathematik/database/Bieberbach.html (108 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Their professional fame is some of the world's top topologists, had pointed out a gap in his proof, tied to mathematical proofs of significant conjectures, and the rush to one that Rourke could not fill.
		The Bieberbach conjecture In March 1986, British mathematician Colin Rourke and his stu- is a statement about the coefficients of power series that represent dent Eduardo Rtgo, from Portugal, announced that they had proved analytic functions with certain properties.
		In his proof, de Branges had proved a conjecture verifying the proof, which ran to dozens of pages in manuscript form, first proposed by I. Milin, who happened to be in Leningrad at the was to find mathematicians willing to take the time from their own time.
	www.amsta.leeds.ac.uk /~robert/1825/projects/text4b-5.txt (806 words)

	Some Systems Theorems Arising From The Bieberbach Conjecture (Site not responding. Last check: 2007-10-08)
		This paper describes how one proof of the Bieberbach conjecture is remarkably parallel to considerations in robust performance of a class of systems.
		The purpose of this paper is to describe the system theoretic component of the proof of the Bieberbach conjecture.
		Our objective in the paper is not to actually give a full proof of the Bieberbach conjecture but to extract the systems ideas which might be of potential use to system theorists and mathematicians.
	www.math.ucsd.edu /~helton/WEENING.html (510 words)

	Springer Online Reference Works (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-08)
		Owing to its simple formulation and profound significance, Bieberbach's conjecture attracted the attention of numerous mathematicians and stimulated the development of different methods in the geometric theory of functions of a complex variable.
		In the laborious progress on the Bieberbach conjecture from 1950 until 1975, M.
		In 1984 the Bieberbach conjecture was established in complete generality by the French-born U.S. mathematician Louis de Branges [a1], [a2].
	eom.springer.de.cob-web.org:8888 /B/b016150.htm (686 words)

	Bieberbach conjecture for the eighth coefficient, Mitsuru Ozawa, Yoshihisa Kubota (Site not responding. Last check: 2007-10-08)
		Bieberbach conjecture for the eighth coefficient, Mitsuru Ozawa, Yoshihisa Kubota
		[9] OZAWA, M., On the Bieberbach conjecture for the sixth coefficient.
		[13] PEDERSON, R. N., A proof of the Bieberbach conjecture for the sixth coefficient Arch.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.kmj/1138846582 (186 words)

	Kent Pearce -- Curriculum Vitae: Specialization And Statement Of Research Interests (Site not responding. Last check: 2007-10-08)
		Their development in the 70's, of course, was aimed at attacking the Bieberbach conjecture.
		While they did not resolve the Bieberbach conjecture (L. deBrange in the early 80's solved the conjecture using alternate techniques), they provided a powerful synthesis for resolving there-to-fore fragmented problems in the theory.
		First, it is becoming increasingly clear from our recent work on the Krzy conjecture, the Gram polynomials, the Szegö polynomials, etc. that fluency/literacy in the language/domain of Special Functions is a program area that I need to cultivate in order to address yet others of these unresolved open problems.
	www.math.ttu.edu /~pearce/vita-int.shtml (517 words)

	LRB \| Karl Sabbagh : The Strange Case of Louis de Branges (Site not responding. Last check: 2007-10-08)
		Not only that: there are uncanny similarities between the initial reaction of other mathematicians to his claim to have proved the Bieberbach Conjecture then, and the unwillingness now to consider that he might have proved the Riemann Hypothesis.
		A third, in a festschrift to celebrate de Branges's Bieberbach Conjecture proof, said: 'In March of 1984 the message began to travel.
		Louis de Branges was claiming a proof of the Bieberbach Conjecture.
	www.lrb.co.uk /v26/n14/print/sabb01_.html (2810 words)

	[No title]
		Of course a couple of other minor issues, not mentioned in the book, have been settled as well, such as the 4-Color conjecture, the Fermat last theorem conjecture, the Bieberbach conjecture about schlicht functions, and many more that I don't recall, don't understand, and/or don't know about or have forgotten.
		While I am on the subject of conjectures, my friends in Algebraic Geometry told me about some sort of conjecture involving the Jacobian and something or other to do with polynomials in lots of variables.
		The Jacobian conjecture is that if J is a nonzero constant, then f is an isomorphism.
	www.math.niu.edu /~rusin/known-math/99/conjectures (1062 words)

	Louis de Branges de Bourcia
		He is best known for proving the long-standing Bieberbach conjecture in 1984, now called De Branges' theorem.
		De Branges' proof of the Bieberbach conjecture was not initially accepted by the mathematical community.
		Rumors of his proof began to circulate in March 1984, but many mathematicians were sceptical, because de Branges had earlier announced some false results, including a claimed proof of the invariant subspace conjecture in 1964 (incidentally, he recently published a new claimed proof for this conjecture on his website).
	www.parsnava.com /biography/sdmc_Louis_de_Branges_de_Bourcia (531 words)

	Multivalent Functions - Cambridge University Press
		The class of multivalent functions is an important one in complex analysis.
		They occur for example in the proof of De Branges' theorem which, in 1985, settled the long-standing Bieberbach conjecture.
		The second edition of Professor Hayman's celebrated book is the first book to contain a full and self-contained proof of this result, with a new chapter devoted to it.
	www.cambridge.org /aus/catalogue/catalogue.asp?isbn=0521460263 (145 words)

	Springer Online Reference Works
		With the aid of the outer area theorem (1916), L.
		Bieberbach obtained precise upper and lower bounds for
		He also found the exact value of the Koebe constant.
	eom.springer.de /u/u095620.htm (1483 words)

	Bieberbach conjecture (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-08)
		Bieberbach conjecture - Google News (via CobWeb/3.1 planetlab2.tamu.edu)
		In complex analysis, the Bieberbach conjecture states a necessary condition on an analytic function to map the unit disk injectively to itself.
		The conjecture was stated in 1916 by Bieberbach but proved only in 1985 by de Branges, with a proof that was subsequently much shortened by others.
	publicliterature.org.cob-web.org:8888 /en/wikipedia/b/bi/bieberbach_conjecture.html (89 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		In that time, a huge number of papers discussing the conjecture and its related problems were inspired.
		In 1989, Professor Gong wrote and published a short book in Chinese, The Bieberbach Conjecture, outlining the history of the related problems and de Branges' proof.
		Open problems and a large number of new mathematical results motivated by the Bieberbach conjecture are included.
	www.yurinsha.com /314/p2.html (362 words)

	Robertson Conjecture (Site not responding. Last check: 2007-10-08)
		A conjecture due to M. Robertson (1936) which treats a
		Bieberbach Conjecture and follows in turn from the
		Milin Conjecture, thus establishing the Robertson conjecture and hence implying the truth of the
	www.math.sdu.edu.cn /mathency/math/r/r351.htm (43 words)

	Topics: Mathematical Conjectures (Site not responding. Last check: 2007-10-08)
		Idea: An algebraic topology conjecture, proven by Quillen and Sullivan using étale cohomology.
		Idea: A relationship between perfect squares and modular arithmetic conjectured by R Langlands in the 1960's; proved in 2000 (@ NAMS).
		Idea: A conjecture on how prime numbers are distributed amongst other numbers; All of the nontrivial zeros of the Riemann zeta function
	www.phy.olemiss.edu /~luca/Topics/m/math_conjectures.html (358 words)

	Cornell Math - Math 613, Fall 2002
		This will be a second course in complex variables focusing on the theory of conformal mappings of the plane.
		The starting point will be a review of the Riemann mapping theorem followed by: Koebe 1/4 Theorem, distortion theorems, extremal distance (extremal length), harmonic measure and boundary behavior (Beurling projection theorem, Makarov's theorem), Loewner differential equation and applications to Bieberbach conjecture.
		If there is time, we may discuss deBranges' proof of the Bieberbach conjecture.
	www.math.cornell.edu /Courses/GradCourses/FA02/613.html (198 words)

	BBC NEWS \| Science/Nature \| Greatest maths problem 'solved'
		It has defeated mathematicians since 1859 when Bernhard Riemann published a conjecture about how prime numbers were distributed amongst other numbers.
		Since then the problem has attracted a cult following among mathematicians, but after nearly 150 years no one has ever definitively proven Riemann's theory to be either true or false.
		De Branges solved another problem in mathematics - the Bieberbach Conjecture - about 20 years ago.
	news.bbc.co.uk /2/hi/science/nature/3794813.stm (349 words)

	Introduction
		Since confirmation of the Bieberbach conjecture by de Branges, perhaps the outstanding open problem in complex analysis is that of finding the exact value of the Bloch constant.
		It is conjectured that the correct value of
		Finally we show that this class of mappings does not depend on the quasiregularity.
	www.3dfractals.com /bloch/node1.html (376 words)

	Read This: Mathematical Conversations
		To prove the Mordell Conjecture, you will learn from this article, Faltings first had to prove two equally important conjectures, the Shafarevich Conjecture and the Tate Conjecture.
		It is theoretically possible, believe it or not, to cut an orange into a finite number of pieces that can then be reassembled to produce two oranges, each having the same size and volume as the first one.
		Then you can read about the last 100 days of the Bieberbach conjecture, about the origins of the Max-Planck-Institute for Mathematics in Bonn, the war of the frogs and mice between Hilbert and Brouwer, and a rare update on the status of the 23 Problems of David Hilbert and the recent developments around them.
	www.maa.org /reviews/mathconv.html (991 words)

	Conformal and Quasiconformal Maps
		A proof of the Bieberbach conjecture (L. de Branges.
		Acta Math 154 (1985) no 1-2 pp 137-152) (We really care about the simplified proof as presented in "The Bieberbach conjecture" (L. Weinstein.
		The proof of the Milin result and further details can be traced down via the survey article "The Bieberbach conjecture and Milin functionals" (A. Grinshpan.
	www.math.ucla.edu /~thiele/workshop3/topics.html (806 words)

	Category:Conjectures - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-08)
		In mathematics, a conjecture is a mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or disprove.
		For more information, see the article about conjecture.
		There is one subcategory to this category shown below (more may be shown on subsequent pages).
	en.wikipedia.org.cob-web.org:8888 /wiki/Category:Conjectures (103 words)

	MATH RIOTS PROVE FUN INCALCULABLE
		A few bookstores had windows smashed and shelves stripped, and vacant lots glowed with burning piles of old dissertations.
		But overall we can feel relief that it was nothing -- nothing -- compared to the outbreak of exuberant thuggery that occurred in 1984 after Louis DeBranges finally proved the Bieberbach Conjecture.
		We were ready for them this time." When word hit Wednesday that Fermat's Last Theorem had fallen, a massive show of force from law enforcement at universities all around the country headed off a repeat of the festive looting sprees that have become the traditional accompaniment to triumphant breakthroughs in higher mathematics.
	danny.oz.au /danny/humour/fermat (864 words)

	[No title]
		Since, at least for us, equalities are much easier to prove than inequalities, the actual \fIproof\fR of the \fIequality\fR is minor compared to its conception.
		.SP1 [AG2] _____, \fIInequalities for polynomials\fR, in: " `The Bieberbach Conjecture`, Proceedings of the symposium on the occasion of the proof" (A. Baernstein et.
		.SP1 [deB] Louis de Branges, \fIA proof of the Bieberbach conjecture\fR, Acta Math.
	www.math.rutgers.edu /~zeilberg/TROFF/asgas.troff (837 words)

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