Estimates for invariant metrics near a non-semipositive boundary point

TL;DR

This paper analyzes the behavior of invariant metrics near boundary points with negative Levi form eigenvalues, introducing a new pseudometric and providing precise growth estimates.

Contribution

It provides exact growth rates of invariant metrics near non-semipositive boundary points and introduces a new invariant pseudometric suited for this setting.

Findings

Precise growth estimates of invariant metrics near non-semipositive boundary points

Introduction of a new invariant pseudometric with useful properties

Analysis applicable to boundary points with negative Levi form eigenvalues

Abstract

We find the precise growth of some invariant metrics near a point on the boundary of a domain where the Levi form has at least one negative eigenvalue. We also introduce a new invariant pseudometric which is convenient in this context, and give some of its general properties.