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Math Help - Looking for Biholomorphic map

  1. #1
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    Looking for Biholomorphic map

    Hi, Im trying to find biholomorphic maps. More explicitly, let D be the unit disk. Im looking for for biholomorphic maps that transform

    a) the ellipse E = \{z=x+iy | (x/a)^2 +(y/b)^2 < 1\}
    b) the half-strip \{z \in \mathbb{C} | 0 < Re z < 1, Im z > 0\}

    into D. Any help for either a) or b) is appreciated.
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  2. #2
    Super Member girdav's Avatar
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    a) Put f(x+iy):=ax+iby.
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  3. #3
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    I thought about that, but I dont think its holomorphic (although its real differentiable) since the Cauchy Riemann differential equations do not hold.
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