Mixed volume forms and a complex equation of Monge--Amp\`ere type on K\"ahler manifolds of positive curvature
Izvestiya. Mathematics , Tome 74 (2010) no. 3, pp. 501-514.

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We consider a generalization of the Calabi problem. In the analytic set-up on a Kähler manifold, it leads to a complex Monge–Ampère equation containing the mixed discriminant of the given and unknown metrics. We obtain sufficient conditions for its solubility in the case when the Kähler manifold is δ-pinched (δ>1/2).
Mots-clés : Kähler manifold, Monge–Ampère equation.
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V. N. Kokarev. Mixed volume forms and a complex equation of Monge--Amp\`ere type on K\"ahler manifolds of positive curvature. Izvestiya. Mathematics , Tome 74 (2010) no. 3, pp. 501-514. https://geodesic-test.mathdoc.fr/item/IM2_2010_74_3_a3/

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