A note on the asymptotic behavior of conformal metrics with negative curvatures near isolated singularities

Abstract

The asymptotic behavior of conformal metrics with negative curvatures near an isolated singularity was described up to the second order derivatives by Kraus and Roth, 2008. We refine Kraus and Roth's result for the second order mixed derivatives and give estimates for higher order derivatives near an isolated singularity. We also compute the Minda-type limits for SK-metrics near the singularity. Combining these limits with Ahlfors' lemma, we provide two observations for SK-metrics.