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

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...

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

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...

manifold) Arakelyan's theorem (complex analysis) Area theorem (conformal mapping) (complex analysis) Arithmetic Riemann–Roch theorem (algebraic geometry)...

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...

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...

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...

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

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

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...

"Some remarks on conformal representation", Annals of Mathematics, 16: 72–76, doi:10.2307/1968044 Nehari, Zeev (1952), Conformal mapping, Dover, pp. 248–249...

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

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

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...

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

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...

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

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...

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,...

analytic functions Montel's theorem Poincaré metric Schwarz lemma Riemann mapping theorem Carathéodory's theorem (conformal mapping) Böttcher's equation Orbit...

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

on the unit disk. The disk and the upper half plane are related by a conformal map, and isometries are given by Möbius transformations. A third representation...

arbitrarily-sized circles: these give rise to discrete analogs of conformal mapping, Riemann surfaces and the like. In the two-dimensional Euclidean plane...

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

The ideas of combinatorial conformal geometry that underlie Cannon's proof of the "combinatorial Riemann mapping theorem", were applied by Cannon, Floyd...

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