He was known for his research on complex analysis and in particular on conformal maps.

If instead angles are preserved, one speaks of conformal maps.

An important family of examples of conformal maps comes from complex analysis.

A conformal map is a transformation of the plane preserving angles.

By means of conformal maps, the formula can be generalized to any simply connected open set.

In mathematics, a conformal map is a function which preserves angles.

Here are examples of conformal maps understood as deforming pictures.

Conformal maps give rise to Kleinian groups, for example.

But not all such matrices produce rotations: conformal maps on S are also included.

A conformal map is called that because it conforms to the principle of angle-preservation.

"Conformal maps," as such distortions are known, have been extensively studied by mathematicians.

A lot of useful information can be understood concerning the conformal map by picturing its pull-back.

The family of conformal maps in three dimensions is very poor, and essentially contains only Möbius transformations.

The projection from the Euclidean plane to a sphere without a point is a diffeomorphism and even a conformal map.

Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size.

Carathéodory's theorem - A conformal map extends continuously to the boundary.

This is equivalent to preservation of angles, the defining characteristic of a conformal map.

One example of a fluid dynamic application of a conformal map is the Joukowsky transform.

In General Relativity, conformal maps are the simplest and thus most common type of causal transformations.

On simply connected planar domains, there is a close connection between harmonic measure and the theory of conformal maps.

These are conformal maps of the unit disk onto the complex plane with a Jordan arc connecting a finite point to omitted.

For example, stereographic projection of a sphere onto the plane augmented with a point at infinity is a conformal map.

Finally, invoking the reciprocal of a biquaternion, Girard described conformal maps on spacetime.

Holomorphic functions are also sometimes referred to as regular functions or as conformal maps.

Every Möbius transformation is a bijective conformal map of the Riemann sphere to itself.