Characterization of Monge-Ampere measures with Holder continuous potentials

Details Characterization of Monge-Ampere measures with Holder continuous potentials Characterization of Monge-Ampere measures with Holder continuous potentials

2012-04-22

arxiv.org/abs/1204.4883v1

Mathematics

Complex Variables

17 pages

Scientific paper

We show that the complex Monge-Ampere equation on a compact Kaehler manifold (X,\omega) of dimension n admits a Holder continuous omega-psh solution if and only if its right-hand side is a positive measure with Holder continuous super-potential. This property is true in particular when the measure has locally Holder continuous potentials or when it belongs to the Sobolev space W^{2n/p-2+epsilon,p}(X) or to the Besov space B^{epsilon-2}_{\infty,\infty}(X) for some epsilon>0 and p>1.

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