Abstract
The aim of this paper is to give a classification of the solutions ϕ = ϕ ( x , y ) of the fourth-order nonlinear equation ϕ y y ρ x x − 2 ϕ x y ρ x y + ϕ x x ρ y y = 0 , ρ = ( det ( ∇ 2 ϕ ) ) − 3 / 4 , in a punctured domain which are C 2 at the singularity. We prove that this kind of solutions either have a removable singularity or are asymptotic to rotationally symmetric solutions near the singularity. A geometric description of solutions which are not C 1 at the singularity is also given.
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