The paper proves the Datar-Mete-Song conjecture: a pair of Kähler classes is semi-stable exactly when its minimal J-slope equals the topological J-slope.
and Zeriahi, A.,Monge–Amp` ere equations in big cohomology classes, Acta Math
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On the Datar-Mete-Song minimal slope conjecture
The paper proves the Datar-Mete-Song conjecture: a pair of Kähler classes is semi-stable exactly when its minimal J-slope equals the topological J-slope.