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Topic: Uniformization theorem

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	Citations: On Thurston's uniformization theorem for three-dimensional manifolds - Morgan (ResearchIndex)
		Citations: On Thurston's uniformization theorem for three-dimensional manifolds - Morgan (ResearchIndex)
		Morgan, On Thurston's uniformization theorem for three-dimensional manifolds, in : J.Morgan, H.Bass, The Smith Conjecture, A.P., 1984, 37-126.
		Theorem 1.1 of [14] states, among other things, that if is any proper 1 manifold in a compact, connected 3 manifold Y such that meets every 2 sphere in Y at least twice and every projective plane in Y at least once, then is....
	citeseer.ist.psu.edu /context/121354/0 (2502 words)

	Springer Online Reference Works
		The existence of a resolving system (the local uniformization theorem) was proved for arbitrary varieties over a field of characteristic zero (see [1]), and also for two-dimensional varieties over any field and three-dimensional varieties over an algebraically closed field of characteristic other than 2, 3 or 5 (see [2]).
		In the general case the local uniformization theorem implies the existence of a finite resolving system (see [3]).
		For (local) uniformization in analytic geometry and in the theory of functions of a complex variable (Riemann surfaces) cf.
	eom.springer.de /L/l060230.htm (295 words)

	Springer Online Reference Works
		Therefore the problem of uniformization of algebraic curves is contained in the problem of uniformization of Riemann surfaces.
		In the uniformization of Riemann surfaces of finite type, the possible Kleinian groups may be classified.
		Teichmüller space) allows one to prove the possibility of simultaneous uniformization of several Riemann surfaces by a single Kleinian group, as well as that of all Riemann surfaces of a given type (cf.
	eom.springer.de /u/u095290.htm (888 words)

	PlanetMath: proof of the uniformization theorem
		We postpone the proof of this fact to the end of the present paragraph and we continue with the proof of the uniformization theorem.
		"proof of the uniformization theorem" is owned by Simone.
		This is version 11 of proof of the uniformization theorem, born on 2006-01-09, modified 2006-11-17.
	planetmath.org /encyclopedia/ProofOfTheUniformizationTheorem.html (289 words)

	Riemann mapping theorem - Wikipedia, the free encyclopedia
		The theorem was stated (under the assumption that the boundary of U is piecewise smooth) by Bernhard Riemann in 1851 in his PhD thesis.
		The Riemann mapping theorem is the easiest way to prove that any two simply connected domains in the plane are homeomorphic.
		The Riemann mapping theorem can be generalized to the context of Riemann surfaces: If U is a simply-connected open subset of a Riemann surface, then U is biholomorphic to one of the following: the Riemann sphere, the complex plane or the open unit disk.
	en.wikipedia.org /wiki/Riemann_mapping_theorem (1040 words)

	The Riemann Mapping Theorem and the Uniformization Theorem
		The classification of simply connected Riemann surfaces is given by the Uniformization theorem.
		3 (Poincaré-Koebe Uniformization Theorem) Any simply connected Riemann sphere is biholomorphically equivalent to the Riemann sphere, the complex plane or the unit disc.
		Using the Uniformization theorem one can approach the question of classification of annuli from a different point of view.
	www.math.tifr.res.in /~pablo/teichmuller/node12.html (295 words)

	Amazon.com: "Uniformization Theorem": Key Phrase page (Site not responding. Last check: 2007-09-12)
		In modified form, Dirichlet's Principle is central to one of the derivations of the Uniformization Theorem, v.
		CHAPTER 5 The Ricci flow on surfaces One of the triumphs of nineteenth-century mathematics was the Uniformization Theorem, which implies that every smooth surface admits an essentially unique conformal metric of constant curvature.
		Theorem 5.1 (Uniformization Theorem) Any simply connected Riemann surface is conformally isomorphic either to the plane C. Key Phrases in this book: Uniformization Theorem, parabolic exhaustion, taut manifold, ergodic points, holomorphic chain, meromorphic mappings, forward invariant set, polynomial diffeomorphisms, repulsive fixed point, holomorphic sectional curvature, attractive fixed point, hyperbolic set (See more)
	www.amazon.com /phrase/Uniformization-Theorem (542 words)

	Riemann Mapping Theorem \| World of Mathematics
		One of the central results in the subject of complex analysis, the Riemann mapping theorem unifies the areas of algebra, geometry, and topology.
		The "uniformization theorem" says that any closed surface with no boundary has one of only three types of conformal geometry.
		The absence of other possibilities stems directly from the Riemann mapping theorem, because the geometry of the surface is first "lifted" to a planar covering space and then mapped by Riemann's theorem to the unit disk.
	www.bookrags.com /research/riemann-mapping-theorem-wom (834 words)

	Citations: Koebe uniformization and circle packings - He, Schramm, points (ResearchIndex) (Site not responding. Last check: 2007-09-12)
		Uniformization in the countable case Recall that a circle domain is a domain D such that each connected component of D is a circle or a point.
		Theorem (Countable Koebe Uniformization) 14] Let D ae C be a domain, and suppose that C(D) is countable.
		....connected, Koebe s uniformization theorem tells us that D is conformally homeomorphic to some circle domain D, a domain whose boundary components are circles and points.
	citeseer.ist.psu.edu /context/473390/0 (1633 words)

	The aim of uniformization (Site not responding. Last check: 2007-09-12)
		The uniformization theorem in two dimensions is a very powerful result, for both differential geometry and topology.
		The theorem has not been proved yet, but there are no counterexamples, and a large number of proofs for special cases.
		What is important here is that this flow generalizes to three dimensions such that the fixed points of the flow are the eight homogeneous geometries plus certain ``instanton" configurations, which describe ``necks" between three-manifolds.
	pdg.cecm.sfu.ca /~warp/java/uniform/node2.html (344 words)

	Courses in the Department of Mathematics
		Hartogs’ Theorem), a deeper study of Riemann surfaces, the uniformization theorem, the Dirichlet problem in higher dimensions, differential equations in a complex domain and the Riemann-Hilbert problem, Hardy spaces.
		Inverse and implicit function theorems, transversality, Sard’s theorem and the Whitney embedding theorem.
		Geodesics and the associated variational formalism (formulas for the 1st and 2nd variation of length), the exponential map, completeness, and the influence of curvature on the structure of a manifold (positive versus negative curvature).
	catalogs.uchicago.edu /divisions/math-courses.html (2661 words)

	The Thurston Project
		The subject of study is uniformization theorems in differential geometry.
		In particular, we're using a proposition by Jack and Eric (to be detailed later), that uses BF field theory as a method of `flowing' the geometry of a manifold to a homogeneous one.
		In two dimensions, this leads to the well-known uniformization theorem, ie that all compact orientable Riemann surfaces are just distortions of homogeneous surfaces with n handles.
	pdg.cecm.sfu.ca /~warp/uniform.html (842 words)

	Abstract (Site not responding. Last check: 2007-09-12)
		Boundaries of Gromov hyperbolic spaces and (generalized) uniformization of metric 2-spheres.
		In spirit, this is an attempt to generalize the classical uniformization theorem to a metric space setting.
		Poincare inequalities on metric spaces) that have appeared in work by Heinonen-Koskela, Semmes, and Cheeger, to prove uniformization theorems and answer a question of Semmes.
	www.math.columbia.edu /~ikofman/abstracts/kleiner.html (142 words)

	Réunion d'hiver 2000 de la SMC
		Later, he used this theorem to prove resolution of singularities for surfaces in characteristic 0.
		K of arbitrary characteristic admits local uniformization, provided that the sum of the rational rank of its value group and the transcendence degree of its residue field over K is equal to the transcendence degree of F
		K with respect to the patch topology, simultaneous local uniformization of any finite number of them might open a way to pass from local uniformization to resolution of singularities.
	www.cms.math.ca /Events/winter00/abs/ag-f.html (2248 words)

	Candel, Gómez-Mont: Uniformization of the leaves of a rational vector field
		Candel, Alberto; Gómez-Mont, X. Uniformization of the leaves of a rational vector field.
		We study the analytic structure of the leaves of a holomorphic foliation by curves on a compact complex manifold.
		GHYS, Gauss-Bonnet Theorem for 2-dimensional foliations, J. of Funct.
	www.numdam.org /numdam-bin/item?id=AIF_1995__45_4_1123_0 (174 words)

	WSEAS -- Perelman (Site not responding. Last check: 2007-09-12)
		Fermat's Last Theorem, but possibly even more far-reaching.
		temperature; it ensures that concentrations of elevated temperature will spread out until a uniform temperature is achieved throughout an object.
		The big prize for him is proving his theorem.
	worldses.org /perelman (1968 words)

	Descriptions of spring 2003 courses in the Rutgers-New Brunswick Math Graduate Program
		Riemann mapping theorem, Picard's theorem, Kobayashi hyperbolic metric and the geometric interpretation of the Schwartz lemma;
		Riemann surfaces, Divisors, sheaf and cohomology, Riemann-Roch theorem on compact Riemann surfaces, Hodge theory, and the uniformization theorem for non compact Riemann surfaces, if time permits.
		These ideas are applied using the method of separation of variables to solve partial differential equations, including the heat equation, the wave equation, and the Laplace equation.
	www.math.rutgers.edu /grad/courses/spring_2003_descriptions.html (2457 words)

	TEICHMÜLLERTHEORY
		It was Teichmüller who realized that introducing a new relation, based on quasiconformal mappings (and some homotopy conditions) one gets a space, known as the Teichmüller space, which is simpler to study than the Riemann space.
		This new space is the universal covering space of Riemann space; the mapping class group (see Nielsen's theorem 1.33) becomes the covering group.
		Thus one reduces the study of Riemann space to the study of Teichmüller space and the mapping class group.
	www.math.tifr.res.in /~pablo/teichmuller/node11.html (229 words)

	Suggested outline (Site not responding. Last check: 2007-09-12)
		Show how these two results could be used to compute the torsion subgroup of a given elliptic curve group E(Q).
		Prove the Weak Mordell-Weil Theorem (finiteness of E(Q)/2E(Q)).
		Show that the weak Mordell-Weil theorem, together with the existence of such a height function will prove the theorem.
	www.math.columbia.edu /~boris/teaching/sp05/outline.html (237 words)

	Amazon.com: "uniformization property": Key Phrase page (Site not responding. Last check: 2007-09-12)
		We say that (r7, A)-uniformixation holds or that 77 has the A-uniformization property, if every A-coloring of 77 can be uniformized.
		F has the number uniformization property if for ang R C_ X x N. R E F(X x N).
		The next important property is an "uniformization property" which states that semi-recursive sets are graphs of recursive operations.
	www.amazon.com /phrase/uniformization-property (525 words)

	Ahlfors-Bers Colloquium 1998 - Stony Brook
		The problem is much more difficult when the boundary of M is compressible, and we will discuss some additional necessary (conjecturally sufficient?) conditions in this case.
		Abstract: The proof of Thurston's Orbifold theorem requires a Margulis type theorem describing the thin part of a hyperbolic 3-manifold with cone-type singularities.
		We will describe a strong version of the Soul Theorem for these objects.
	www.math.sunysb.edu /events/abc/speakers.html (288 words)

	[No title]
		What theorem of multivariable calculus is this similar to?
		(conformal coordinates give it a complex structure, so it becomes a Riemann surface.) State the theorem of uniformization for Riemann Surfaces.
		Maximum-modulus principle ------------------------- Hadamard 3-circles theorem, generalize to annuli with slits missing.
	www.princeton.edu /~missouri/Generals/generals/complex.txt (1516 words)

	Descriptions of spring 2005 courses in the Rutgers-New Brunswick Math Graduate Program
		Topics to be covered: the Riesz representation theorem for positive linear functionals on C(X), the Birkhoff ergodic theorem, the Marcinkiewicz interpolation theorem, the Riesz-Thorin interpolation theorem, the Fourier transform and elementary theory of singular integrals.
		We outline the proofs of these results, including the positive mass theorem of Schoen and Yau on which the proof of the last case relies.
		This course will be an introduction to Lie groups, beginning with the general linear group and the other classical groups (the unitary, orthogonal and symplectic groups) and finishing with the Weyl character formula and the Borel-Weil theorem for the irreducible representations of a compact, connected Lie group such as U(n).
	www.math.rutgers.edu /grad/courses/spring_2005_descriptions.html (3510 words)

	Cornell Math - MATH 612, Spring 2005
		A graduate course in complex analysis, covering Cauchy's theorem, residues, Riemann mapping theorem, harmonic functions.
		Other topics will be discussed, to be determined with the class in the first week.
		Possible topics: Riemann surfaces and the uniformization theorem, several complex variables, analytic number theory, Nevanlinna theory.
	www.math.cornell.edu /~www/Courses/GradCourses/SP05/612.html (54 words)

	UNT Department of Mathematics: People: Faculty
		Working with functions of p-adic numbers is sort of halfway in between algebra and analysis, so the idea is that studying p-adic problems might provide insights into why the existence of many rational solutions to equations seems to be related to the existence functional solutions.
		Another area Cherry works in is known as Nevanlinna theory, which extends the Fundamental Theorem of Algebra to meromorphic functions.
		Finally, Cherry continues to have research interests in classical complex analysis, particularly the use of geometric methods to better understand various inequalities.
	www.math.unt.edu /faculty/cherry.shtml (236 words)

	[No title] (Site not responding. Last check: 2007-09-12)
		It's very difficult) State and sketch the proof of Riemann mapping theorem.
		Then Washnitzer said Uniformization theorem for bounded domains is as easy as this!
		Show that eigenvlues of a skewsymmetric matrix is not real(they are pure imaginary) find conditions for the existence of solution for exp(A)=B, B given matrix.
	www.princeton.edu /~missouri/Generals/generals/rastegar_arash (395 words)

	Complex Analysis (Site not responding. Last check: 2007-09-12)
		The second part includes various more specialized topics as the argument principle, the Schwarz lemma and hyperbolic geometry, the Poisson integral, and the Riemann mapping theorem.
		The third part consists of a selection of topics designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis.
		Topics selected include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces.
	www.booksmatter.com /b0387950699.htm (289 words)

	William A. Cherry
		Working with functions of p-adic numbers is sort of halfway in between algebra and analysis, so the idea is it might help us understand how functional solutions are related to rational solutions.
		Another area I work in is Nevanlinna theory, which extends the Fundamental Theorem of Algebra to meromorphic functions.
		Finally, I have research interests in classical complex analysis, particularly using geometric methods to better understand various inequalities.
	wcherry.math.unt.edu /index.html (362 words)

	Math 220 General Information (Site not responding. Last check: 2007-09-12)
		This first part includes complex differentiation and integration, Cauchy's theorem, Residue theorem, argument of principle, power series, normal family, Picard's theorems, harmonic functions, conformal mappings.
		Hopefully, we can also cover the uniformization theorem on both compact and noncompact Riemann surfaces.
		There will be a midterm and a final exam.
	www.math.ucsd.edu /~lni/math220 (219 words)

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