Localization of invariant metrics

摘要

The localization of the Green function, higher order and singular Kobayashi metrics, and the Azukawa metric near a local peak point of an open set in $ mathbb{C}^n $ are proved. Localization results for the Bergman kernel (on the diagonal), Bergman metric and its holomorphic sectional curvature near a local peak point of an open pseudoconvex set in $ mathbb{C}^n $ are also obtained.