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

Given N ≥ 2, we completely classify solutions to the anisotropic -Liouville equation (formula presented) under the finite mass condition (formula presented). Here ΔHN 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].