Hessian equations on closed Hermitian manifolds

DOI10.2140/pjm.2017.291.485zbMath1392.35141arXiv1501.03553OpenAlexW3098918089MaRDI QIDQ2406430

Dekai Zhang

Publication date: 27 September 2017

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.03553

zbMATH Keywords

a priori estimatesHessian equationsclosed Hermitian manifolds

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Nonlinear elliptic equations (35J60)

Related Items (26)

On uniform estimate of complex elliptic equations on closed Hermitian manifolds ⋮ Fully non-linear elliptic equations on compact manifolds with a flat hyperkähler metric ⋮ The Fu-Yau equation with negative slope parameter ⋮ The complex Hessian equations with gradient terms on Hermitian manifolds ⋮ The Fu-Yau equation in higher dimensions ⋮ Continuous solutions to complex Hessian equations on Hermitian manifolds ⋮ Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds ⋮ The Dirichlet problem for Monge-Ampère type equations on Hermitian manifolds ⋮ The parabolic flows for complex quotient equations ⋮ Monge-Ampère type equations on almost Hermitian manifolds ⋮ Hessian equations of Krylov type on Kähler manifolds ⋮ The weak solutions to complex Hessian equations ⋮ Fully non-linear elliptic equations on compact almost Hermitian manifolds ⋮ On \(L^{\infty}\) estimate for complex Hessian quotient equations on compact Kähler manifolds ⋮ Second order estimates for complex Hessian equations with gradient terms on both sides ⋮ Unnamed Item ⋮ Fully non-linear degenerate elliptic equations in complex geometry ⋮ Estimates for the Hessian equation on compact almost Hermitian manifolds ⋮ Unnamed Item ⋮ A class of the non-degenerate complex quotient equations on compact Kähler manifolds ⋮ Second order estimates for complex Hessian equations on Hermitian manifolds ⋮ Fu-Yau Hessian equations ⋮ Second order estimates for a class of complex Hessian equations on Hermitian manifolds ⋮ Regularity of degenerate \(k\)-Hessian equations on closed Hermitian manifolds ⋮ Transverse fully nonlinear equations on Sasakian manifolds and applications ⋮ Hessian equations of Krylov type on compact Hermitian manifolds

Cites Work

• Unnamed Item
• Geometric flows and Strominger systems
• On the evolution of a Hermitian metric by its Chern-Ricci form
• A second order estimate for complex Hess equations on a compact Kähler manifold
• On uniform estimate of complex elliptic equations on closed Hermitian manifolds
• The Fu-Yau equation with negative slope parameter
• On estimates for the Fu-Yau generalization of a Strominger system
• The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation
• Complex Monge-Ampère equations and totally real submanifolds
• The Monge-Ampère equation for (𝑛-1)-plurisubharmonic functions on a compact Kähler manifold
• Liouville and Calabi-Yau type theorems for complex Hessian equations
• A Priori Estimates for Complex Monge-Ampere Equation on Hermitian Manifolds
• The complex Monge-Ampère equation on compact Hermitian manifolds
• The k-Hessian Equation
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• On some inequalities for elementary symmetric functions
• A variational theory of the Hessian equation

This page was built for publication: Hessian equations on closed Hermitian manifolds