A Riemann mapping theorem for two-connected domains in the plane

Details A Riemann mapping theorem for two-connected domains in the plane A Riemann mapping theorem for two-connected domains in the plane

2008-01-15

arxiv.org/abs/0801.2376v1

Mathematics

Complex Variables

10 pages

Scientific paper

We show how to express a conformal map of a general two connected domain in the plane such that neither boundary component is a point to a representative domain which has the virtue of having an explicit algebraic Bergman kernel function. We shall explain why the representative domain is the best analogue of the unit disc in the two connected setting. The conformal map will be given as a simple and explicit algebraic function of an Ahlfors map of the domain associated to a specially chosen point. It will follow that the conformal map can be found by solving the same extremal problem that determines a Riemann map in the simply connected case.

Affiliated with

Also associated with

No associations

Rating

A Riemann mapping theorem for two-connected domains in the plane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Riemann mapping theorem for two-connected domains in the plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Riemann mapping theorem for two-connected domains in the plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-159268