On stability and continuity of bounded solutions of degenerate complex Monge–Ampère equations over compact Kähler manifolds

By S. Dinew, Zhou Zhang. 2010

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Abstract We obtain a stability estimate for the degenerate complex Monge–Ampere operator which generalizes a result of Kolodziej (2003) [12] . In particular, we obtain the optimal stability exponent and also treat the case when the right-hand side is a general Borel measure satisfying certain regularity conditions. Moreover, our result holds for functions plurisubharmonic with respect to a big form, thus generalizing the Kahler form setting in Kolodziej (2003) [12] . Independently, we also provide more detail for the proof in Zhang (2006) [18] on continuity of the solution with respect to a special big form when the right-hand side is L p -measure with p > 1 .

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e6204026c506fac7f2f1fef59b0b932ccdc3403f