The infimum of the Nijenhuis energy

Abstract

We prove that on any symplectic manifold whose symplectic form represents a rational cohomology class there exists a sequence of compatible almost complex structures whose Nijenhuis energy (the $L^2$-norm of the Nijenhuis tensor) tends to zero. The sequence is obtained by stretching the neck around a Donaldson hypersurface.Comment: 6 pages; updated with minor corrections to agree with published versio