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.
Classification: 53C55, 35J96, 32U40
Keywords: Weak solutions, Hölder continuous, Monge–Ampère, Compact Hermitian manifold
@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{\textendash}Amp\`ere} equation on compact {Hermitian} manifolds},
journal = {Annales de l'Institut Fourier},
pages = {2951--2964},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {68},
number = {7},
year = {2018},
doi = {10.5802/aif.3232},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3232/}
}
TY - JOUR TI - Hölder continuous solutions of the Monge–Ampère equation on compact Hermitian manifolds JO - Annales de l'Institut Fourier PY - 2018 DA - 2018/// SP - 2951 EP - 2964 VL - 68 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3232/ UR - https://doi.org/10.5802/aif.3232 DO - 10.5802/aif.3232 LA - en ID - AIF_2018__68_7_2951_0 ER -
%0 Journal Article %T Hölder continuous solutions of the Monge–Ampère equation on compact Hermitian manifolds %J Annales de l'Institut Fourier %D 2018 %P 2951-2964 %V 68 %N 7 %I Association des Annales de l’institut Fourier %U https://doi.org/10.5802/aif.3232 %R 10.5802/aif.3232 %G en %F 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, 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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