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Regularity of A Complex Monge-Amp\`{e}re Equation on Hermitian Manifolds

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Preprint
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arXiv ID: 1311.4463
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arXiv
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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.

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