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Complex Hessian Equations on Some Compact Kähler Manifolds

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  • Asma Jbilou

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.

Suggested Citation

  • Asma Jbilou, 2012. "Complex Hessian Equations on Some Compact Kähler Manifolds," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-48, December.
  • Handle: RePEc:hin:jijmms:350183
    DOI: 10.1155/2012/350183
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