The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds

Abstract

We study the Dirichlet problem of a class of fully nonlinear elliptic equations on Hermitian manifolds and derive a priori $C^2$ estimates which depend on the initial data on manifolds, the admissible subsolutions and the upper bound of the gradients of the solutions. In some special cases, we obtain the gradient estimates, and hence we can solve the corresponding Dirichlet problem with admissible subsolutions. We also study the Hessian quotient equations and $(m-1,m-1)$-Hessian quotient equations on compact Hermitian manifolds without boundary.

arXiv comment45 pages

References in corpus (7)

• The Space of Kähler metrics (II)
• The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
• $C^{2,\alpha }$ estimates for nonlinear elliptic equations in complex and almost complex geometry
• On the $C^{1,1}$ regularity of geodesics in the space of Kähler metrics
• Complex Monge-Ampere equations on Hermitian manifolds
• Form-type Calabi-Yau equations on Kähler manifolds of nonnegative orthogonal bisectional curvature
• Regularity of fully non-linear elliptic equations on Hermitian manifolds. II

Cited by in corpus (2)

• Second order estimates for fully nonlinear elliptic equations with gradient terms on Hermitian manifolds
• Second order estimates for a class of complex Hessian equations on Hermitian manifolds