Gromov hyperbolicity of pseudo-convex Levi corank one domains

TL;DR

This paper proves that certain bounded pseudo-convex domains with Levi form of corank one are Gromov hyperbolic under the Kobayashi metric, extending previous results to a broader class of domains.

Contribution

It establishes Gromov hyperbolicity for a new class of pseudo-convex domains with Levi form of corank one, generalizing prior work by Zimmer and Fiacchi.

Findings

Bounded pseudo-convex domains of finite type with Levi corank one are Gromov hyperbolic.

Stability of Kobayashi metrics under scaling processes.

Extension of Gromov hyperbolicity results to broader domain classes.

Abstract

After a study of the Kobayashi metrics on certain scaled domains, we show the stabilities of the infinitesimal Kobayashi metrics and the integrated distances in different scaling processes. As an application, we prove that bounded pseudo-convex domains of finite type where the Levi form of every boundary point has corank one are Gromov hyperbolic with respect to the Kobayashi metric. The results in this note generalize Zimmer's and Fiacchi's related works on Gromov hyperbolicity of weakly pseudo-convex domains.