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Hölder continuity of solutions to the complex Monge–Ampère equation with the right-hand side in L p: the case of compact Kähler manifolds

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Abstract

We prove that on compact Kähler manifolds solutions to the complex Monge–Ampère equation, with the right-hand side in L p, p > 1, are Hölder continuous.

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Correspondence to Sławomir Kołodziej.

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Partially supported by Polish ministerial grants N201 3679 33, 189/6 PR EU/2007/7 and EU grant MTKD-CT-2006-042360.

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Kołodziej, S. Hölder continuity of solutions to the complex Monge–Ampère equation with the right-hand side in L p: the case of compact Kähler manifolds. Math. Ann. 342, 379–386 (2008). https://doi.org/10.1007/s00208-008-0239-y

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  • DOI: https://doi.org/10.1007/s00208-008-0239-y

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