In mathematics, the uniformization theorem states that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces:...

studied by Koebe who proved in 1910, as a generalization of the uniformization theorem, that every such surface is conformally equivalent to either the...

mathematics, the simultaneous uniformization theorem, proved by Bers (1960), states that it is possible to simultaneously uniformize two different Riemann surfaces...

onto D {\displaystyle D} . Koebe's uniformization theorem for normal families also generalizes to yield uniformizers f {\displaystyle f} for multiply-connected...

according to their universal cover. The uniformization theorem is a generalization of the Riemann mapping theorem from proper simply connected open subsets...

Look up uniformization in Wiktionary, the free dictionary. Uniformization may refer to: Uniformization (set theory), a mathematical concept in set theory...

geometric proof, which yields a stronger geometric result, is the uniformization theorem. This was originally proven only for Riemann surfaces in the 1880s...

In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with...

whose genus is at least 1 {\displaystyle 1} . The Uniformization theorem and the Gauss–Bonnet theorem can both be applied to orientable Riemann surfaces...

In the context of compact Riemann surfaces X, via the Riemann uniformization theorem, this can be seen as a distinction between the surfaces of different...

In mathematics, the uniform limit theorem states that the uniform limit of any sequence of continuous functions is continuous. More precisely, let X be...

infamously known as "Cauchy's wrong theorem". The uniform limit theorem shows that a stronger form of convergence, uniform convergence, is needed to ensure...

known proofs of the circle packing theorem. Paul Koebe's original proof is based on his conformal uniformization theorem saying that a finitely connected...

Lazarus Fuchs. By the uniformization theorem, every Riemann surface is either elliptic, parabolic or hyperbolic. More precisely this theorem states that a Riemann...

theorem Toponogov theorem Sphere theorem Hodge theory Uniformization theorem Yamabe problem Killing vector field Myers-Steenrod theorem Hodge star operator...

Low-dimensional topology is strongly geometric, as reflected in the uniformization theorem in 2 dimensions – every surface admits a constant curvature metric;...

Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly approximated as closely as...

bounded interval has a uniformly convergent subsequence. The main condition is the equicontinuity of the family of functions. The theorem is the basis of many...

exclusively with the complex numbers, his most important results being on the uniformization of Riemann surfaces in a series of four papers in 1907–1909. He did...

at most 3. Local uniformization in positive characteristic seems to be much harder. Abhyankar (1956, 1966) proved local uniformization in all characteristics...

In descriptive set theory the Jankov–von Neumann uniformization theorem is a result saying that every measurable relation on a pair of standard Borel spaces...

Low-dimensional topology is strongly geometric, as reflected in the uniformization theorem in 2 dimensions – every surface admits a constant curvature metric;...

homeomorphism. This is a consequence of the uniformization theorem for surfaces and the geometrization theorem for 3-manifolds proved by Perelman. A hyperbolic...

structure that can be associated with it. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply connected...

prove a grand uniformization theorem that would establish the new theory more completely. Klein succeeded in formulating such a theorem and in describing...

quasi-Fuchsian groups of the first kind is described by the simultaneous uniformization theorem of Bers. Fricke, Robert; Klein, Felix (1897), Vorlesungen über die...

2-dimensional manifold (surface) admits a constant curvature metric, by the uniformization theorem. There are 3 such curvatures (positive, zero, and negative). This...

MR 1031909, S2CID 122626150 Morgan, John W. (1984), "On Thurston's uniformization theorem for three-dimensional manifolds", in Morgan, John W.; Bass, Hyman...

Various uniformization theorems can be proved using the equation, including the measurable Riemann mapping theorem and the simultaneous uniformization theorem...

Riemann surface. The classification essentially follows from the uniformization theorem, and is as follows: g = 0: C P 1 {\displaystyle \mathbb {CP} ^{1}}...