A Liouville theorem for Möbius invariant equations (Q6110234)

The authors characterize Möbius invariant differential operators of second order in dimension two as \(F(A^u)\), where \(A^u\) is a suitable \(2\times2\) matrix operator of second order. The main result is a Liouville type theorem for the equation \(F(A^u)=1\), where \(F\) depends on the eigenvalues \(\lambda(A^u)\in \Gamma\), where \(\Gamma\) is an open convex symmetric cone intermediate between the quarter-plane \(\{\lambda_1>0,\lambda_2>0\}\) (included) and the half-plane \(\{\lambda_1+\lambda_2>0\}\) (excluded), without no additional assumptions on the behaviour of \(u\) at infinity.