Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds

Hiep, Pham Hoang

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 ${\omega }_u^n$ 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 ${\omega }_u^n$ is moderate if $u$ is Hölder continuous. We prove a theorem which is a partial converse to this result.

Classification : 32W20, 32Q15
Keywords: Hölder continuity, complex Monge-Ampère operator, $\omega $-plurisubharmonic functions, compact Kähler manifolds
Mot clés : continuité de Hölder, opérateur complexe de Monge-Ampère, fonctions $\omega $-pluriharmoniques, variétés de Kähler compactes

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