Hölder continuous solutions of the Monge–Ampère equation on compact Hermitian manifolds  [ Solutions continues Höldériennes de l’équation de Monge–Ampère sur les variétés hermitiennes compactes ]
Annales de l'Institut Fourier, Tome 68 (2018) no. 7, pp. 2951-2964.

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.

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.

Publié le : 2019-05-24
DOI : https://doi.org/10.5802/aif.3232
Classification : 53C55,  35J96,  32U40
Mots clés : solutions faibles, continue Höldérienne, Monge–Ampère, variété hermitienne compacte
@article{AIF_2018__68_7_2951_0,
     author = {Ko\l odziej, S\l awomir and Nguyen, Ngoc Cuong},
     title = {H\"older continuous solutions of the Monge--Amp\`ere equation on compact Hermitian manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {2951--2964},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {7},
     year = {2018},
     doi = {10.5802/aif.3232},
     language = {en},
     url = {archive.numdam.org/item/AIF_2018__68_7_2951_0/}
}
Kołodziej, Sławomir; Nguyen, Ngoc Cuong. Hölder continuous solutions of the Monge–Ampère equation on compact Hermitian manifolds. Annales de l'Institut Fourier, Tome 68 (2018) no. 7, pp. 2951-2964. doi : 10.5802/aif.3232. http://archive.numdam.org/item/AIF_2018__68_7_2951_0/

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