Gromov hyperbolicity of strongly pseudoconvex almost complex manifolds

TL;DR

This paper proves that smooth, relatively compact, strongly pseudoconvex domains in almost complex manifolds are Gromov hyperbolic, extending geometric analysis in complex and almost complex settings.

Contribution

It establishes Gromov hyperbolicity for strongly pseudoconvex domains in almost complex manifolds, a significant extension of known results in complex geometry.

Findings

Domains are connected and Gromov hyperbolic

Extension of hyperbolicity results to almost complex manifolds

Provides geometric insights into the structure of pseudoconvex domains

Abstract

Let $D=\{\rho < 0\}$ be a smooth relatively compact domain in an almost complex manifold $(M,J)$, where $\rho$ is a smooth defining function of $D$, strictly $J$-plurisubharmonic in a neighborhood of the closure $\overline{D}$ of $D$. We prove that $D$ has a connected boundary and is Gromov hyperbolic.