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I read somewhere that in 2D, the Möbius transformations do not represent all the possible conformal transformations, while according to Liouville's theorem, in spaces of dimension greater than 2 all the conformal transformation can be expressed as combinations of scaling/translation/rotation/inversion (=Möbius transformations).

Can anyone mention what are the conformal transformations of the plane that cannot be "captured" by Möbius transformations?

Thanks.

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# Conformal transformations and Möbius transformations

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