Sharp estimates of the Kobayashi metric and Gromov hyperbolicity

TL;DR

This paper provides precise estimates of the Kobayashi metric in almost complex manifolds and demonstrates the Gromov hyperbolicity of certain domains using boundary asymptotics.

Contribution

It introduces sharp boundary estimates of the Kobayashi metric in almost complex domains and establishes Gromov hyperbolicity based on asymptotic analysis.

Findings

Sharp Kobayashi metric estimates near boundary points

Gromov hyperbolicity of the domain D

Asymptotic description of the domain and structure J

Abstract

Let D be a smooth relatively compact and strictly J-pseudoconvex domain in a four dimensional almost complex manifold (M,J). We give sharp estimates of the Kobayashi metric. Our approach is based on an asymptotic quantitative description of both the domain D and the almost complex structure J near a boundary point. Following Z.M.Balogh and M.Bonk, these sharp estimates provide the Gromov hyperbolicity of the domain D.