Regularity of A Complex Monge-Amp\`{e}re Equation on Hermitian Manifolds
- Authors
- Type
- Preprint
- Publication Date
- Nov 18, 2013
- Submission Date
- Nov 18, 2013
- Identifiers
- arXiv ID: 1311.4463
- Source
- arXiv
- License
- Yellow
- External links
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-Amp\`{e}re equation is smooth under an assumption on the background Hermitian metric $\hat{\omega}$. This generalizes a result of Sz\'{e}kelyhidi and Tosatti on K\"{a}hler manifolds.