of conformal mappings, the area theorem gives an inequality satisfied by the power series coefficients of certain conformal mappings. The theorem is called...

Riemann mapping theorem Schwarz–Christoffel mapping – a conformal transformation of the upper half-plane onto the interior of a simple polygon. Conformal radius...

Carathéodory's theorem is a theorem in complex analysis, named after Constantin Carathéodory, which extends the Riemann mapping theorem. The theorem, published...

in conformal mapping theory, see area theorem (conformal mapping). This disambiguation page lists articles associated with the title Area theorem. If...

Arakelyan's theorem (complex analysis) Area theorem (conformal mapping) (complex analysis) Beurling–Lax theorem (Hardy spaces) Bloch's theorem (complex analysis)...

is a conformal map in the mathematical sense. For example, if two roads cross each other at a 39° angle, their images on a map with a conformal projection...

space exactly when the subdivision rule is "conformal", as described in the combinatorial Riemann mapping theorem. Applications of subdivision rules. Islamic...

Riemann mapping theorem, formulated by Bernhard Riemann in 1851, states that, for any two open topological disks in the plane, there is a conformal map from...

remarks on conformal representation", Annals of Mathematics, 16 (1/4): 72–76, doi:10.2307/1968044, JSTOR 1968044 Nehari, Zeev (1952), Conformal mapping, Dover...

is called conformal when it preserves angles. Hyperbolic angle is defined using area under y = 1/x. Since squeeze mappings preserve areas of transformed...

in one complex dimension (such as conformality) do not carry over. The Riemann mapping theorem about the conformal relationship of certain domains in...

theory is the Riemann mapping theorem. The following are some of the most important topics in geometric function theory: A conformal map is a function which...

generators are all conformal. The translation z → z + b is a change of origin and makes no difference to angle. To see that z → az is conformal, consider the...

torus (total angle 2π/3). These are the only conformal equivalence classes of flat tori that have any conformal automorphisms other than those generated by...

(1960) and Conformal invariants (1973). He made decisive contributions to meromorphic curves, value distribution theory, Riemann surfaces, conformal geometry...

In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard...

from the complex plane itself admits a conformal and bijective map to the open unit disk. One bijective conformal map from the open unit disk to the open...

It maps circles on the sphere to circles or lines on the plane, and is conformal, meaning that it preserves angles at which curves meet and thus locally...

Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact Riemann surface...

identity mapping, for k = − 1 {\displaystyle k=-1} one gets the reflection at the center, For 1 / k {\displaystyle 1/k} one gets the inverse mapping defined...

Riemann mapping theorem and the simultaneous uniformization theorem. The existence of conformal weldings can also be derived using the Beltrami equation...

dz.\,} The proof of this statement uses the Cauchy integral theorem and like that theorem, it only requires f to be complex differentiable. Since 1 /...

group but also determines the Riemann surface up to conformal equivalence. By the uniformization theorem, every compact Riemann surface has simply connected...

of the Gauss equation, the formula for second variation of area, and the Gauss-Bonnet theorem, Schoen and Yau were able to rule out the existence of several...

boundaries of domains in complex manifolds. Conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. Differential...

straight, but the disadvantage that angles are distorted (the mapping is not conformal), and also circles are not represented as circles. The distance...

1909–1910. The works of Osgood dealt with complex analysis, in particular conformal mapping and uniformization of analytic functions, and calculus of variations...

geometry related to simple polygons include Schwarz–Christoffel mapping, used to find conformal maps involving simple polygons, polygonalization of point sets...

geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive solid geometry Contact geometry Convex geometry...

In spherical geometry, Lexell's theorem holds that every spherical triangle with the same surface area on a fixed base has its apex on a small circle,...