In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U {\displaystyle U} and V {\displaystyle V} be open subsets of R n {\displaystyle \mathbb {R} ^{n}} .

Mar 5, 2025 · A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves local angles. An analytic function is conformal at any point where it has a nonzero derivative.

Conformal Mapping is a transformation from z-plane to w-plane, preserving the angles between the curves. Learn more about conformal mapping with geometrical explanations.

Conformal Mappings In the previous chapters we studied automorphisms of D, and the geometric behavior of holomorphic maps from D to D using the Poincar´e metric.

As we’ve seen, once we have flows or harmonic functions on one region, we can use conformal maps to map them to other regions. In this section we will offer a number of conformal maps between various regions.

In this topic we will look at the geometric notion of conformal maps. It will turn out that analytic functions are automatically conformal. Once we have understood the general notion, we will look at a specific family of conformal maps called fractional linear transformations and, in particular at their geometric properties.

May 13, 2021 · Conformal mapping is a mathematical technique used to convert (or map) one mathematical problem and solution into another. It involves the study of complex variables. Complex variables are combinations of real and imaginary numbers, which is …

Paul Garrett: Conformal mapping (November 23, 2014) Three points on a circle determine the circle completely. A line in C can be viewed determined by two points on it in C, and inevitably passing through 1. The group of linear fractional transformation actions

Jun 4, 2020 · A large part is played by conformal mappings of two-dimensional domains not only on planar surfaces but also for domains lying on smooth surfaces. Examples of such conformal mappings are given by stereographic projection and Mercator projection of …

The idea of a global conformal map is that we embed R(p,q) into a suitable completion or compactification, X, such that there is a sufficiently large collection of conformal automorphisms of X.