Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds
Annales de l'Institut Fourier, Volume 60 (2010) no. 5, p. 1857-1869

We study Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds. T. C. Dinh, V.A. Nguyen and N. Sibony have shown that the measure ω u n is moderate if u is Hölder continuous. We prove a theorem which is a partial converse to this result.

Nous étudions la continuité de Hölder des solutions des équations de Monge-Ampère sur des variétés Kählériennes compactes. T. C. Dinh, V.A. Nguyen et N. Sibony ont prouvé que ω u n est modéré si u est Hölder-continue. Nous démontrons dans quelques cas la réciproque de ce résultat.

DOI : https://doi.org/10.5802/aif.2574
Classification:  32W20,  32Q15
Keywords: Hölder continuity, complex Monge-Ampère operator, ω-plurisubharmonic functions, compact Kähler manifolds
@article{AIF_2010__60_5_1857_0,
     author = {Hiep, Pham Hoang},
     title = {H\"older continuity of solutions to the Monge-Amp\`ere equations on compact K\"ahler manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {5},
     year = {2010},
     pages = {1857-1869},
     doi = {10.5802/aif.2574},
     mrnumber = {2766232},
     zbl = {1208.32033},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2010__60_5_1857_0}
}
Hiep, Pham Hoang. Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds. Annales de l'Institut Fourier, Volume 60 (2010) no. 5, pp. 1857-1869. doi : 10.5802/aif.2574. http://www.numdam.org/item/AIF_2010__60_5_1857_0/

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