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Continuity of Monge–Ampère Potentials with Prescribed Singularities

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Abstract

We study the continuity of solutions to complex Monge–Ampère equations with prescribed singularity type. This generalizes the previous results of Di Nezza–Lu and the author Dang (Int Math Res Not 14:11180-11201, 2022), Di Nezza and Lu (J Reine Angew Math 727:145-167, 2017). As an application, we can run the pluripotential Monge–Ampère flows in Dang (J Funct Anal 282(6):65, 2022) starting at a current with prescribed singularities.

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Acknowledgements

I am grateful to Tamás Darvas for interesting exchanges. Many thanks to Antonio Trusiani for explaining the paper [26]. I thank the referee for the useful comments, which improved the presentation of the paper. This work is partially supported by the ANR project PARAPLUI.

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  1. The Abdus Salam International Centre for Theoretical Physics (ICTP), Str. Costiera, 11, 34151, Trieste, TS, Italy

    Quang-Tuan Dang

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  1. Quang-Tuan Dang
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Dang, QT. Continuity of Monge–Ampère Potentials with Prescribed Singularities. J Geom Anal 33, 318 (2023). https://doi.org/10.1007/s12220-023-01388-6

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