Existence and stability of foliations by J-holomorphic spheres

TL;DR

This paper investigates the existence and stability of J-holomorphic foliations in higher dimensions, revealing they are not stable under large perturbations, unlike in four dimensions.

Contribution

It provides new insights into the stability of holomorphic foliations in higher dimensions and presents an example demonstrating their instability under significant perturbations.

Findings

J-holomorphic foliations are not stable under large perturbations in dimensions greater than 4

The paper offers an example illustrating the instability of these foliations in higher dimensions

Stability results differ significantly from the four-dimensional case

Abstract

We study the existence and stability of holomorphic foliations in dimension greater than 4 under perturbations of the underlying almost complex structure. An example is given to show that, unlike in dimension 4, J-holomorphic foliations are not stable under large perturbations of almost complex structure.