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Extending Di Nezza–Lu’s approach [ 16 ] to the setting of big cohomology classes, we prove that solutions of degenerate complex Monge–Ampère equations on compact Kähler manifolds are continuous on a Zariski open set. This allows us to show that singular Kähler–Einstein metrics on log canonical varieties of general type have continuous potentials on the ample locus outside of the non-klt part.

Continuity of Monge–Ampère Potentials in Big Cohomology Classes