Communications in Analysis and Geometry

Volume 22 (2014)

Number 5

Regularity of a complex Monge-Ampère equation on Hermitian manifolds

Pages: 833 – 856



Xiaolan Nie (School of Mathematics, University of Minnesota, Minneapolis, Minn., U.S.A.)


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.

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