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arXiv · 2003.08417

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

Chinh H. Lu·Trong-Thuc Phung·Tât-Dat Tô
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Abstract

Let $(X,ω)$ 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.

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Chinh H. Lu, Trong-Thuc Phung, Tât-Dat Tô. 2020-11-14. Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds. https://arxiv.org/abs/2003.08417

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