Regularity of A Complex Monge-Ampère Equation on Hermitian Manifolds

Abstract

We obtain higher order estimates for a parabolic flow on a compact Hermitian manifold. As an application, we prove that a bounded $\hat{\omega }$-plurisubharmonic solution of an elliptic complex Monge-Ampère equation is smooth under an assumption on the background Hermitian metric $\hat{\omega }$. This generalizes a result of Székelyhidi and Tosatti on Kähler manifolds.

16 pages

References in corpus (4)

• The Kahler-Ricci flow through singularities
• Pluripotential estimates on compact Hermitian manifolds
• Local Calabi and curvature estimates for the Chern-Ricci flow
• Complex Monge-Ampere equations on Hermitian manifolds

Cited by in corpus (2)

• Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds
• Long time existence of the (n-1)-plurisubharmonic flow