Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds

Abstract

Let $(X,\omega )$ be a compact Hermitian manifold. We establish a stability result for solutions to complex Monge-Ampère equations with right-hand side in $L^p$, $p>1$. Using this we prove that the solutions are Hölder continuous with the same exponent as in the Kähler case \cite{DDGKPZ14}. Our techniques also apply to the setting of big cohomology classes on compact Kähler manifolds.

final version to appear in Annales de l'Institut Fourier