Riemann sphere

Riemann spheres have been used, together with digital video, for this purpose.

The complex projective line is also called the Riemann sphere.

The set is the Riemann sphere, which is of major importance in complex analysis.

However, is still undefined on the Riemann sphere, but defined in wheels.

Using these definitions, f becomes a continuous function from the Riemann sphere to itself.

The Riemann sphere is a matematical model of the extended complex plane.

This space noted is isomorphic to the Riemann sphere.

Now, fix a basepoint b on the Riemann sphere away from the poles.

Ahlfors showed that if the limit set is not the whole Riemann sphere then it has measure 0.

Suppose is a harmonic function into the Riemann sphere.

Fix some point p on the Riemann sphere.

The Riemann sphere has many uses in physics.

Consequently, the period domain is the Riemann sphere.

Suppose that z is a holomorphic local coordinate for the Riemann sphere.

The group may also be represented in terms of a set of functions defined on the Riemann sphere.

However, the Riemann sphere is not merely a topological sphere.

This treatment of the Riemann sphere connects most readily to projective geometry.

Thus the unit sphere is diffeomorphic to the Riemann sphere.

With no punctures, it is the Riemann sphere, which is elliptic.

In general, the two fixed points may be any two distinct points on the Riemann sphere.

Also the Riemann sphere can be extended to a wheel by adjoining an element .

Intuitively, the transition maps indicate how to glue two planes together to form the Riemann sphere.

It suffices to compute its integral over the Riemann sphere:

All other points flow along a family of circles which is nested between the two fixed points on the Riemann sphere.

The Riemann sphere is one example.