Hölder continuous solutions of the Monge–Ampère equation on compact Hermitian manifolds
Annales de l'Institut Fourier, Volume 68 (2018) no. 7, pp. 2951-2964.

We show that a positive Borel measure of positive finite total mass, on a compact Hermitian manifold, admits a Hölder continuous quasi-plurisubharmonic solution to the Monge–Ampère equation if and only if it is dominated locally by Monge–Ampère measures of Hölder continuous plurisubharmonic functions.

Nous prouvons qu’une mesure de Borel positive avec la masse totale finie, sur une variété hermitienne compacte, admet une solution quasi plurisousharmonique de l’équation de Monge–Ampère si et seulement si elle est dominée localement par des mesures de Monge–Ampère des fonctions plurisousharmoniques continues Höldériennes.

Published online:
DOI: 10.5802/aif.3232
Classification: 53C55,  35J96,  32U40
Keywords: Weak solutions, Hölder continuous, Monge–Ampère, Compact Hermitian manifold
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Kołodziej, Sławomir; Nguyen, Ngoc Cuong. Hölder continuous solutions of the Monge–Ampère equation on compact Hermitian manifolds. Annales de l'Institut Fourier, Volume 68 (2018) no. 7, pp. 2951-2964. doi : 10.5802/aif.3232. https://aif.centre-mersenne.org/articles/10.5802/aif.3232/

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