This article is cited in 4 papers

Mixed volume forms and a complex equation of Monge–Ampère type on Kähler manifolds of positive curvature

V. N. Kokarev

Samara State University

Abstract: 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.

UDC: 514.772

MSC: 32W20, 32Q15

Received: 14.09.2007

DOI: 10.4213/im2728

 English version: Izvestiya: Mathematics, 2010, 74:3, 501–514

Bibliographic databases:

• 
• 
• 
• 
• 
• 
•