Resumen de On absolutely conformal mappings
David Kalaj, Miodrag Mateljevic
Let be a domain in Rn. It is proved that, if u 2 C1(;Rn) and there holds the formula kru(x)kn = nn=2j detru(x)j in , then for n ¸ 3 u is a restriction of a MÄobius transformation, and for n = 2, u is an analytic function. This extends, partially, the well-known Liouville theorem ([?]), wich states that if u 2 ACLn(;Rn), n ¸ 3, and the condition kru(x)kn = nn=2 detru(x) is satis¯ed a.e. in , then u is a restriction of a MÄobius transformation.
