I have a question about conformal mapping. I am wanting to map annuli to some other simple domain (probably rectangular). I have an image of my problem below
In image A. we see a standard annulus which has been cut radially. We can easily map this annulus to a rectangle using the transformation log(z).
However, if I cut the annulus horizontally, as in image B. then this transformation no longer maps to a "nice" domain.
Questions:
Is there a name for chopped annuli as in A. and B.?
Is there any nice conformal transformation for B.?
Thanks v much!