Stability of the vanishing of the $\overline\partial_b$-cohomology under small horizontal perturbations of the CR structure in compact abstract q-concave CR manifolds

TL;DR

This paper investigates how small horizontal perturbations of CR structures on compact q-concave CR manifolds affect the stability of the vanishing of certain -cohomology groups, showing that such properties are preserved under these perturbations.

Contribution

It demonstrates the stability of the vanishing of -cohomology groups under small horizontal perturbations of the CR structure on compact q-concave CR manifolds.

Findings

Vanishing of -cohomology groups is stable under small horizontal perturbations.

Concavity properties are preserved by such perturbations.

Finiteness of certain -cohomology groups remains unchanged.

Abstract

We consider perturbations of CR structures which preserve the complex tangent bundle. For a compact generic CR manifold its concavity properties and hence the finiteness of some $\overline\partial_b$-cohomology groups are also preserved by such perturbations of the CR structure. Here we study the stability of the vanishing of these groups.