Classification of Solutions to the Anisotropic N-Liouville Equation in ℝN

Given N≥ 2, we completely classify solutions to the anisotropic N-Liouville equation align* &-ΔNH\,u=eᵘ \ RN,align* under the finite mass condition ∫ _RN eᵘ\,dx<+∞. Here Δ NH is the so-called Finsler N-Laplacian induced by a positively homogeneous function H. As a consequence in the planar case $N=2$, we give an affirmative answer to a conjecture made in [ 53].