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arXiv · 1211.0106

Poincaré-Lelong formula, $J$-analytic subsets and Lelong numbers of currents on almost complex manifolds

Fredj Elkhadhra
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Abstract

In this paper, we first establish a Poincaré-Lelong type formula in the almost complex setting. Then, after introducing the notion of $J$-analytic subsets, we study the restriction of a closed positive current defined in an almost complex manifold $(M,J)$ on a $J$-analytic subset. Finally, we prove that the Lelong numbers of a plurisubharmonic current defined on an almost complex manifold are independent of the coordinate systems.

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Fredj Elkhadhra. 2012-11-01. Poincaré-Lelong formula, $J$-analytic subsets and Lelong numbers of currents on almost complex manifolds. https://arxiv.org/abs/1211.0106

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