Complex Hessian Equations on Some Compact Kähler Manifolds

Asma Jbilou

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-48

Abstract:

On a compact connected -dimensional Kähler manifold with Kähler form , given a smooth function and an integer , we want to solve uniquely in the equation , relying on the notion of -positivity for (the extreme cases are solved: by (Yau in 1978), and trivially). We solve by the continuity method the corresponding complex elliptic th Hessian equation, more difficult to solve than the Calabi-Yau equation ( ), under the assumption that the holomorphic bisectional curvature of the manifold is nonnegative, required here only to derive an a priori eigenvalues pinching.

Date: 2012
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2012/350183.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2012/350183.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:350183

DOI: 10.1155/2012/350183

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().