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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 3, Pages 65–78 (Mi izv2728)  

This article is cited in 3 scientific papers (total in 3 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.

DOI: https://doi.org/10.4213/im2728

Full text: PDF file (565 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:3, 501–514

Bibliographic databases:

UDC: 514.772
MSC: 32W20, 32Q15
Received: 14.09.2007

Citation: V. N. Kokarev, “Mixed volume forms and a complex equation of Monge–Ampère type on Kähler manifolds of positive curvature”, Izv. RAN. Ser. Mat., 74:3 (2010), 65–78; Izv. Math., 74:3 (2010), 501–514

Citation in format AMSBIB
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  • https://doi.org/10.4213/im2728
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Dinew, S. Kołodziej, “A priori estimates for complex Hessian equations”, Anal. PDE, 7:1 (2014), 227–244  crossref  mathscinet  zmath  isi  scopus
    2. Valentino Tosatti, Yu Wang, Ben Weinkove, Xiaokui Yang, “$C^{2,\alpha}$ estimates for nonlinear elliptic equations in complex and almost complex geometry”, Calc. Var. Partial Differential Equations, 54:1 (2015), 431–453  crossref  mathscinet  zmath  isi  scopus
    3. Tosatti V., Weinkove B., “The Monge-Ampère equation for $(n-1)$-plurisubharmonic functions on a compact Kähler manifold”, J. Am. Math. Soc., 30:2 (2017), 311–346  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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