Higher Order Asymptotic Behavior of Certain Kähler Metrics and Uniformization for Strongly Pseudoconvex Domains

Abstract

Abstract. We provide some relations between CR invariants of boundaries of strongly pseudoconvex domains and higher order asymptotic behavior of certain complete Kähler metrics of given domains. As a consequence, we prove a rigidity theorem of strongly pseudoconvex domains by asymptotic curvature behavior of metrics.