# ANNALES DE L'INSTITUT FOURIER

Stability and Hölder regularity of solutions to complex Monge–Ampère equations on compact Hermitian manifolds
[Stabilité et Continuité Höldérienne des solutions des équations de Monge–Ampère complexes sur des variétés Hermitiennes compactes]
Annales de l'Institut Fourier, Online first, 27 p.

Soit $\left(X,\omega \right)$ une variété Hermitienne compacte de dimension $n$. On établit la stabilité des solutions des équations de Monge–Ampère avec second membre dans ${L}^{p}$, $p>1$. En utilisant ce résultat on montre que les solutions sont continues höldériennes avec le même exposant que celui obtenu dans le cas Kählérien par Demailly-Dinew–Guedj–Kołodziej–Pham–Zeriahi. Notre méthode s’applique également dans le contexte des classes de cohomologie sur une variété Kählérienne.

Let $\left(X,\omega \right)$ 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 by Demailly–Dinew–Guedj–Kołodziej–Pham–Zeriahi. Our techniques also apply to the setting of big cohomology classes on compact Kähler manifolds.

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Révisé le :
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DOI : https://doi.org/10.5802/aif.3436
Classification : 32W20,  32U05,  32Q15
Mots clés : Variété hermitienne, Équation de Monge–Ampère complexe, Stabilité, Principe de comparaison
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author = {Lu, Chinh H. and Phung, Trong-Thuc and T\^o, T\^at-Dat},
title = {Stability and {H\"older} regularity of solutions to complex {Monge{\textendash}Amp\ere} equations on compact {Hermitian} manifolds},
journal = {Annales de l'Institut Fourier},
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year = {2021},
doi = {10.5802/aif.3436},
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note = {Online first},
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Lu, Chinh H.; Phung, Trong-Thuc; Tô, Tât-Dat. Stability and Hölder regularity of solutions to complex Monge–Ampère equations on compact Hermitian manifolds. Annales de l'Institut Fourier, Online first, 27 p.`

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