Geodesic
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 $\delta$-pinched ($\delta>1/2$).
Keywords: Kähler manifold, Monge–Ampère equation. 
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     author = {V. N. Kokarev},
     title = {Mixed volume forms and a complex equation of {Monge--Amp\`ere} type on {K\"ahler} manifolds of positive curvature},
     journal = {Izvestiya. Mathematics },
     pages = {501--514},
     publisher = {mathdoc},
     volume = {74},
     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2010_74_3_a3/}
}
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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. http://geodesic.mathdoc.fr/item/IM2_2010_74_3_a3/