A note on the geometry of pseudoconvex domains of finite type in almost complex manifolds

TL;DR

This paper investigates the geometric properties of pseudoconvex domains of finite type within almost complex manifolds, focusing on the asymptotic behavior of pseudoholomorphic discs near the boundary.

Contribution

It provides new insights into the asymptotic behavior of pseudoholomorphic discs in finite type pseudoconvex domains of almost complex manifolds.

Findings

Asymptotic behavior characterized for pseudoholomorphic discs

Boundary regularity results for pseudoconvex domains

Extension of classical complex analysis results to almost complex setting

Abstract

Let $D=\{\rho<0\}$ be a smooth domain of finite type in an almost complex manifold (M,J) of real dimension four. We assume that the defining function $\rho$ is J-plurisubharmonic on a neighborhood of $\overline{D}$. We study the asymptotic behavior of pseudoholomorphic discs contained in the domain D.