Abstract
We give the first examples of positive closed currents T in \({{\mathbb C}^2}\) with continuous potentials, \({T \wedge T = 0}\), and whose supports do not contain any holomorphic disk. This gives in particular an affirmative answer to a question of Fornæss and Levenberg. We actually construct examples with potential of class C 1,α for all α < 1. This regularity is expected to be essentially optimal.
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Research partially supported by ANR project BERKO
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Dujardin, R. Wermer Examples and Currents. Geom. Funct. Anal. 20, 398–415 (2010). https://doi.org/10.1007/s00039-010-0066-7
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DOI: https://doi.org/10.1007/s00039-010-0066-7