Localization of invariant metrics

Abstract.

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.