Conformal mapping from polygon with circle segments

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SUMMARY

The discussion centers on finding a conformal map from a polygon to the upper half-plane using circle segments instead of straight lines. The Schwarz-Christoffel mapping is identified as the closest established method for this purpose. Participants suggest exploring resources related to conformal mapping and circular arc polygons, emphasizing the importance of specific references for deeper understanding. The mention of the Schwarzian derivative highlights its relevance in this context.

PREREQUISITES
  • Understanding of conformal mapping principles
  • Familiarity with the Schwarz-Christoffel mapping technique
  • Knowledge of circular arc polygons
  • Basic grasp of the Schwarzian derivative
NEXT STEPS
  • Research the Schwarz-Christoffel mapping in detail
  • Explore the properties and applications of circular arc polygons
  • Study the Schwarzian derivative and its implications in conformal mapping
  • Investigate numerical methods for implementing conformal maps with circle segments
USEFUL FOR

Mathematicians, researchers in complex analysis, and anyone interested in advanced topics of conformal mapping and geometric transformations.

Kurret
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I am looking for a conformal map from a "polygon" to eg the upper half plane, which consists of circle segments instead of lines. So for example, it could be a quadrilateral ABCD, but where AB is a circle segment. The closest I can find is the Schwarz-Christoffel mapping.

Anyone has any tips?
 
I don't know about this subject, but I notice that you can find numerous hits by searching for the topic of conformal mapping and "circular arc polygons". (For example: http://en.wikipedia.org/wiki/Schwarzian_derivative mentions circular arc polygons.)

If you find a reference that seems to do what you want and have a specific question about it, there are probably forum members who can explain it.
 

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