  A classical result of Nitsche \cite{Nit57} about the behaviour of the
solutions to the Liouville equation $\Delta u=4 e^{2u}$ near isolated
singularities is generalized to solutions of the Gaussian curvature equation
  $\Delta u=- \kappa(z) e^{2u}$ where $\kappa$ is a negative H\"older
continuous function. As an application a higher--order version of the
Yau--Ahlfors--Schwarz lemma for complete conformal Riemannian metrics is
obtained.
