On the isolated singularities of the solutions of the Gaussian curvature equation for nonnegative curvature

The precise asymptotic behaviour of the solutions to the twodimensional curvature equation $\mathrm{\Delta }u=k(z)e^{2u}$ with $e^{2u}\in L^1$ for bounded nonnegative curvature functions $-k(z)$ near isolated singularities is obtained.