  We show that on a Kahler manifold whether the J-flow converges or not is
independent of the chosen background metric in its Kahler class. On toric
manifolds we give a numerical characterization of when the J-flow converges,
verifying a conjecture of Lejmi and the second author in this case. We also
strengthen existing results on more general inverse $\sigma_{k}$ equations on
Kahler manifolds.

Differential Geometry