An improved Riemann Mapping Theorem and complexity in potential theory

Details An improved Riemann Mapping Theorem and complexity in potential theory An improved Riemann Mapping Theorem and complexity in potential theory

2011-10-04

arxiv.org/abs/1110.0770v1

Mathematics

Complex Variables

23 pages

Scientific paper

We discuss applications of an improvement on the Riemann mapping theorem which replaces the unit disc by another "double quadrature domain," i.e., a domain that is a quadrature domain with respect to both area and boundary arc length measure. Unlike the classic Riemann Mapping Theorem, the improved theorem allows the original domain to be finitely connected, and if the original domain has nice boundary, the biholomorphic map can be taken to be close to the identity, and consequently, the double quadrature domain close to the original domain. We explore some of the parallels between this new theorem and the classic theorem, and some of the similarities between the unit disc and the double quadrature domains that arise here. The new results shed light on the complexity of many of the objects of potential theory in multiply connected domains.

Affiliated with

Also associated with

No associations

Rating

An improved Riemann Mapping Theorem and complexity in potential theory 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 An improved Riemann Mapping Theorem and complexity in potential theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An improved Riemann Mapping Theorem and complexity in potential theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-269980