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A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...

A generalized conformal mapping.

An indirectly conformal mapping, sometimes called an anticonformal mapping, is a mapping that reverses all angles, whereas an isogonal mapping can reverse some angles and ...

Several flavors of the open mapping theorem state: 1. A continuous surjective linear mapping between Banach spaces is an open map. 2. A nonconstant analytic function on a ...

An isogonal mapping is a transformation w=f(z) that preserves the magnitudes of local angles, but not their orientation. A few examples are illustrated above. A conformal ...

Let Y^X be the set of continuous mappings f:X->Y. Then the topological space for Y^X supplied with a compact-open topology is called a mapping space.

A geodesic mapping f:M->N between two Riemannian manifolds is a diffeomorphism sending geodesics of M into geodesics of N, whose inverse also sends geodesics to geodesics ...

Let z_0 be a point in a simply connected region R!=C, where C is the complex plane. Then there is a unique analytic function w=f(z) mapping R one-to-one onto the disk |w|<1 ...

A conformal mapping from the upper half-plane to a polygon.

Asserts the existence and uniqueness of the extremal quasiconformal map between two compact Riemann surfaces of the same genus modulo an equivalence relation.