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

IF 0.8 4区数学 Q2 MATHEMATICS

Annales De L Institut Fourier Pub Date : 2020-03-18 DOI:10.5802/aif.3436

C. H. Lu, Trong Phung, T. Tô

引用次数: 17

Abstract

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

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales De L Institut Fourier 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

1 months

期刊介绍： The Annales de l’Institut Fourier aim at publishing original papers of a high level in all fields of mathematics, either in English or in French. The Editorial Board encourages submission of articles containing an original and important result, or presenting a new proof of a central result in a domain of mathematics. Also, the Annales de l’Institut Fourier being a general purpose journal, highly specialized articles can only be accepted if their exposition makes them accessible to a larger audience.