Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Has anyone any general tips for finding conformal tranformations from a domain to another? For example from $D=\{ z=x+iy | x^2+y^2<1, x^2-x+y^2>0 \}$ to the unit disc. This set is a disc minus a smaller disc, so what should i imagine to try? If someone could provide his reasoning step by step telling what ideas make him use certain transformations (also providing some variants, for example: 'i'd do this because, while if there had been this i would have done that') i would be very grateful, because i don't seem to get a general idea of what is happening. Thanks

share|cite|improve this question
up vote 2 down vote accepted

Looks like the disks are internally tangent at $z=1$. This looks like a special point for this domain. It's a good idea to map the special point to $\infty$ by a fractional linear transformation. This makes both circles a special kind of circles: namely, lines. And the domain becomes a strip.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.