Weighted Boundary Limits of the Generalized Kobayashi-Royden Metrics on Weakly Pseudoconvex Domains

The purpose of this paper is to study the existence of weighted boundary limits of the generalized Kobayashi-Royden metrics on weakly pseudoconvex domains in Cⁿ and to explore the connections between the limits and the Levi invariants. The main result extends Graham’s result on strongly pseudoconvex domains to a large class of weakly pseudoconvex domains.