The asymptotic behavior of the Bergman kernel on pseudoconvex model domains

TL;DR

This paper studies the boundary asymptotics of the Bergman kernel on pseudoconvex model domains, linking it to the geometry of the Newton polyhedron, including both finite and infinite type cases.

Contribution

It provides a detailed analysis of the Bergman kernel's asymptotic behavior on pseudoconvex domains, extending results to infinite type cases using Newton polyhedron geometry.

Findings

Asymptotic formulas for the Bergman kernel at the boundary.

Connection between kernel behavior and Newton polyhedron geometry.

Extension of results to infinite type pseudoconvex domains.

Abstract

In this paper, we investigate the asymptotic behavior of the Bergman kernel at the boundary for some pseudoconvex model domains. This behavior can be described by the geometrical information of the Newton polyhedron of the defining function of the respective domains. We deal with not only the finite type cases but also some infinite type cases.