Families of Monge-Ampère measures with Hölder continuous potentials

Vu, Duc-Viet

doi:10.1090/proc/14076

Families of Monge-Ampère measures with Hölder continuous potentials
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Proc. Amer. Math. Soc. 146 (2018), 4275-4282 Request permission

Abstract:

Let $X$ be a compact Kähler manifold of dimension $n.$ Let $\mathcal {F}$ be a family of probability measures on $X$ whose superpotentials are of uniformly bounded $\mathscr {C}^\alpha$ norms for some fixed constant $\alpha \in (0,1].$ We prove that the corresponding family of solutions of the complex Monge-Ampère equations $(dd^c \varphi + \omega )^n= \mu$ with $\mu \in \mathcal {F}$ is Hölder continuous.

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