Abstract
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 in [19] (M. Lejmi and G. Szekelyhidi, “The $J$-flow and stability”) in this case. We also strengthen existing results on more general inverse $\sigma_k$ equations on Kahler manifolds.
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