# Circles in conformal geometry

We know that conformal transformations of the Riemann sphere (which are general Mobius transformations) transform circles to circles. A similar fact is also true in higher dimensions. So we can say that circle is a concept in the conformal geometry of the spheres. Does there exist a more straightforward definition of circles in conformal geometry? and can one use this concept to give a more elementary proof of Liouville's theorem?