The range of the tangential Cauchy-Riemann system on a CR embedded manifold

TL;DR

This paper proves that compact, pseudoconvex, orientable CR manifolds in complex space bound smooth complex manifolds, establishing the closed range property of the tangential Cauchy-Riemann system.

Contribution

It demonstrates that such CR manifolds always bound complex manifolds in the smooth sense, advancing understanding of the tangential Cauchy-Riemann system.

Findings

CR manifolds bound complex manifolds in the smooth sense

The tangential Cauchy-Riemann system has closed range

Results apply to compact, pseudoconvex, orientable CR manifolds

Abstract

We prove that every compact, pseudoconvex, orientable, CR manifold of $\C^n$, bounds a complex manifold in the $C^\infty$ sense. In particular, the tangential Cauchy-Riemann system has closed range.