J-pluripolar subsets and currents on almost complex manifolds |
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Authors: | Fredj Elkhadhra |
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Institution: | 1. Département de Mathématiques, Faculté des Sciences de Monastir, 5000, Monastir, Tunisia
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Abstract: | We prove that every almost complex submanifold of an almost complex manifold is locally J-pluripolar. This generalizes a result of Rosay for J-holomorphic submanifolds. Our second main result is an almost complex version of El Mir’s theorem for the extension of positive
currents across locally complete pluripolar sets. As a consequence, we extend some results proved by Dabbek–Elkhadhra–El Mir
and Dinh–Sibony in the standard complex case. We also obtain a version of the well-known results of Federer and Bassanelli
for flat and
\mathbb C{\mathbb {C}}-flat currents in the almost complex setting. |
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Keywords: | |
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