Any solution with finite total e^u mass of -Δu=K(x)e^u in a punctured disk satisfies u(x)=α ln|x|+O(1) near the singularity, with α>-2, and the same log asymptotics hold for polyharmonic Q-curvature equations in all dimensions.
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On isolated singularities of the conformal Gaussian curvature equation and $Q$-curvature equation
Any solution with finite total e^u mass of -Δu=K(x)e^u in a punctured disk satisfies u(x)=α ln|x|+O(1) near the singularity, with α>-2, and the same log asymptotics hold for polyharmonic Q-curvature equations in all dimensions.