Abstract
In this paper, we introduce and study natural notions of local continuity/boundedness of super-potentials on \({\mathbb {P}}^k\). Next, we prove an equidistribution theorem of positive closed (p, p)-currents of \({\mathbb {P}}^k\), whose super-potentials are continuous/bounded near an invariant analytic subset, for holomorphic endomorphisms of \({\mathbb {P}}^k\). We also consider the case of regular polynomial automorphisms of \(\mathbb C^k\).
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Acknowledgements
The author would like to thank John Erik Fornæss and Viet Anh Nguyen for helpful discussions and suggestions. The author expresses his thanks to Ngaiming Mok for suggestions. The author also would like to thank the referee for careful reading and for suggestions. Referee’s comments and suggestions were helpful in improving and clarifying the arguments.
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Ahn, T. Local regularity of super-potentials and equidistribution of positive closed currents on \({\mathbb {P}}^k\) . Math. Ann. 371, 1163–1190 (2018). https://doi.org/10.1007/s00208-017-1579-2
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DOI: https://doi.org/10.1007/s00208-017-1579-2