## Is the disk quasiconformally isomorphic to the plane?

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(This question might turn out to be too elementary for this site,
if so I'm sorry, but I can't find the answer anywhere.)

Does there exist a function `$\; f : \{z\in \mathbb{C} : |z| < 1\} \to \mathbb{C} \;$`

such that $f\hspace{.01 in}$ is a quasiconformal bijection and $f^{-1}$ is quasiconformal?

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7
The plane and a disk are not quasiconformally equivalent, see e.g. page 11 in math.qc.edu/~zakeri/papers/ahl-bers.pdf. Incidentally, the inverse of a quasiconformal map is automatically quasiconformal. – Igor Belegradek Sep 20 2011 at 2:08
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