Conformally invariant variational integrals

Let f : G → R n f:G \to {R^n} be quasiregular and I = ∫ F ( x , ∇ u ) d m I = \int {F(x,\nabla \,u)\,dm} a conformally invariant variational integral. Hölder-continuity, Harnack’s inequality and principle are proved for the extremals of I I . Obstacle problems and their connection to subextremals are studied. If u u is an extremal or a subextremal of I I , then u ∘ f u \circ f is again an extremal or a subextremal if an appropriate change in F F is made.