Mobius transformations, the Caratheodory metric, and the objects of complex analysis and potential theory in multiply connected domains

Details Mobius transformations, the Caratheodory metric, and the objects of complex analysis and potential theory in multiply connected domains Mobius transformations, the Caratheodory metric, and the objects of complex analysis and potential theory in multiply connected domains

2002-03-27

arxiv.org/abs/math/0203280v1

Mathematics

Complex Variables

Scientific paper

It is proved that the family of Ahlfors extremal mappings of a multiply connected region in the plane onto the unit disc can be expressed as a rational combination of two fixed Ahlfors mappings in much the same way that the family of Riemann mappings associated to a simply connected region can be expressed in terms of a single such map. The formulas reveal that this family of mappings extends to the double as a real analytic function of both variables. In particular, the infinitesimal Caratheodory metric will be expressed in strikingly simple terms. Similar results are proved for the Green's function, the Poisson kernel, and the Bergman kernel.

Affiliated with

Also associated with

No associations

Rating

Mobius transformations, the Caratheodory metric, and the objects of complex analysis and potential theory in multiply connected domains 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 Mobius transformations, the Caratheodory metric, and the objects of complex analysis and potential theory in multiply connected domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mobius transformations, the Caratheodory metric, and the objects of complex analysis and potential theory in multiply connected domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-238318