Complex Hessian equations on some compact Kähler manifolds

DOI10.1016/j.crma.2009.11.011zbMath1189.53071OpenAlexW1965998491MaRDI QIDQ5897166

Asma Jbilou

Publication date: 12 February 2010

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2009.11.011

zbMATH Keywords

Hessian equationcompact connected Kähler manifold with Kähler formholomorphic bisectional curvature of the manifold is non-negative

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Local differential geometry of Hermitian and Kählerian structures (53B35) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (8)

Fully non-linear elliptic equations on compact manifolds with a flat hyperkähler metric ⋮ Solutions to degenerate complex Hessian equations ⋮ The complex Hessian equations with gradient terms on Hermitian manifolds ⋮ The weak solutions to complex Hessian equations ⋮ The Sobolev inequality for complex Hessian equations ⋮ Unnamed Item ⋮ Complex Hessian equations on some compact Kähler manifolds ⋮ A variational approach to complex Hessian equations in \(\mathbb{C}^n\)

Cites Work

• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Closed Weingarten hypersurfaces in Riemannian manifolds
• On the almost complex analogue of the Calabi-Yau equation
• Elliptic partial differential equations of second order
• On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian
• Métriques riemanniennes et courbure
• Weak solutions to the complex Hessian equation.
• Nonlinear elliptic equations and the complex hessian
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• On some inequalities for elementary symmetric functions
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