Integrability of Rough Almost Complex Structures

TL;DR

This paper extends the classical Newlander-Nirenberg theorem to manifolds with less regular almost complex structures, exploring conditions for integrability and the regularity of holomorphic coordinates.

Contribution

It generalizes integrability criteria to rough almost complex structures with sub-Lipschitz regularity, advancing understanding of complex structures with limited smoothness.

Findings

Extended Newlander-Nirenberg theorem to less regular structures

Analyzed regularity of local holomorphic coordinates in Lipschitz cases

Provided conditions for integrability with rough structures

Abstract

We extend the Newlander-Nirenberg theorem to manifolds with almost complex structures that have somewhat less than Lipschitz regularity. We also discuss the regularity of local holomorphic coordinates in the integrable case, with particular attention to Lipschitz almost complex structures.