# Looking for Biholomorphic map

• May 22nd 2011, 12:33 PM
EinStone
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.
• May 22nd 2011, 01:15 PM
girdav
a) Put $f(x+iy):=ax+iby$.
• May 22nd 2011, 01:17 PM
EinStone
I thought about that, but I dont think its holomorphic (although its real differentiable) since the Cauchy Riemann differential equations do not hold.