紧致Hermitian流形上复杂Monge–Ampère方程解的稳定性和Hölder正则性

Pub Date : 2020-03-18 DOI:10.5802/aif.3436

C. H. Lu, Trong Phung, T. Tô

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引用次数: 17

摘要

设$（X，\omega）$是紧致Hermitian流形。我们建立了$L^p$，$p>1$中具有右手边的复杂Monge-Ampere方程解的稳定性结果。利用这一点，我们证明了解是Holder连续的，其指数与Kahler情况下的指数相同。我们的技术也适用于紧Kahler流形上大上同调类的设置。

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

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

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