On the Gromov hyperbolicity of the Kobayashi metric on strictly pseudoconvex regions in the almost complex case

TL;DR

This paper proves that bounded strictly J-convex regions with the Kobayashi metric are Gromov hyperbolic and explores implications for pseudo-holomorphic map dynamics.

Contribution

It establishes Gromov hyperbolicity of the Kobayashi metric in almost complex strictly convex regions, extending known results to the almost complex setting.

Findings

Bounded strictly J-convex regions are Gromov hyperbolic.

Results apply to the dynamics of pseudo-holomorphic maps.

Extension of hyperbolicity concepts to almost complex geometry.

Abstract

We prove that every bounded strictly $J$-convex region equipped with the Kobayashi metric is hyperbolic in the sense of Gromov. We apply this result to the study of the dynamics of pseudo-holomorphic maps.