On the construction of a complete Kähler-Einstein metric with negative scalar curvature near an isolated log-canonical singularity

In this short note we are concerned with the Kähler-Einstein metrics near cone type log canonical singularities. By two different approaches, construct a metric negative scalar curvature in neighborhood of over Calabi-Yau manifold which is complete towards vertex. This provides local model for further study global on singular varieties. first approach, show that singularity uniformized by complex ball and hence induced from Bergman desired one. second obtain properties Calabi Ansatz. At last, obtained same.