Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds
[Continuité Hölder des solutions des équations de Monge-Ampère sur les variétés Kählériennes]
Hiep, Pham Hoang1
1 University of Education (Dai hoc Su Pham Ha Noi) Department of Mathematics CauGiay, Hanoi (Vietnam)
Annales de l'Institut Fourier, Tome 60 (2010) no. 5, pp. 1857-1869.

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 ωun est modéré si u est Hölder-continue. Nous démontrons dans quelques cas la réciproque de ce résultat.

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 ωun is moderate if u is Hölder continuous. We prove a theorem which is a partial converse to this result.

DOI : 10.5802/aif.2574
Classification : 32W20, 32Q15
Keywords: Hölder continuity, complex Monge-Ampère operator, ω-plurisubharmonic functions, compact Kähler manifolds
Mot clés : continuité de Hölder, opérateur complexe de Monge-Ampère, fonctions ω-pluriharmoniques, variétés de Kähler compactes
Hiep, Pham Hoang 1

1 University of Education (Dai hoc Su Pham Ha Noi) Department of Mathematics CauGiay, Hanoi (Vietnam) 
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Hiep, Pham Hoang. Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds. Annales de l'Institut Fourier, Tome 60 (2010) no. 5, pp. 1857-1869. doi : 10.5802/aif.2574. https://www.numdam.org/articles/10.5802/aif.2574/

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