On the Kahler-Einstein metric at strictly pseudoconvex points

TL;DR

This paper establishes local boundary regularity for complete Kahler-Einstein metrics with negative Ricci curvature at strictly pseudoconvex boundary points and analyzes the asymptotic behavior of their holomorphic bisectional curvatures.

Contribution

It provides new insights into the boundary regularity and curvature behavior of Kahler-Einstein metrics near strictly pseudoconvex points.

Findings

Proves local boundary regularity of Kahler-Einstein metrics

Analyzes asymptotic behavior of holomorphic bisectional curvatures

Enhances understanding of metric behavior near pseudoconvex boundaries

Abstract

We prove a local boundary regularity result for the complete Kahler-Einstein metrics of negative Ricci curvature near strictly pseudoconvex boundary point. We also study the asymptotic behaviour of their holomorphic bisectional curvatures near such points.