## Conformal map of a doubly connected region to an annulus [closed]

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Conformal map of a doubly connected region to an annulus

Hi. I am a Mechanical Engineering student. I'm not good at complex variable theory and having problem with finding conformal mapping of a doubly connected region to an annulus (or vice versa).

I know that the annulus is bounded by two circles with inner radius r and outer radius R and the inner and outer radii are not independent and the ratio R/r must be determined uniqely by the doubly connected region.

My doubly connected region is actually a hollow shape in which the inner and outer boundaries are geometrically similar and concentric. Parametric shape functions of the inner and outer boundaries in x-y plane are expressed as: {X=F(theta), Y=G(theta)}.

I would be really thankful if you could help me over this issue or introduce to me some useful references.

B.G.B

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Duplicate: mathoverflow.net/questions/53082/… – Qiaochu Yuan Jan 24 2011 at 17:56