Lelong-Jensen公式、Demaily-Lelong数和正超电流的加权度
Lelong-Jensen formula, Demailly-Lelong numbers and weighted degree of positive supercurrents
摘要：
这项工作的目标是将斯柯达、德迈利和吉卢菲在复分析中研究的正流的广义Lelong数的概念扩展到实超空间上的弱正超流。然后，我们推广了Lagerberg的结果时，超导是封闭的，以及最近的结果Berglessson的最小超导相关的子流形的$\mathbb{R}^n$。主要工具是著名的Lelong-Jensen公式在超性能主义情况下的一个变体。此外，我们扩展到我们的设置在复分析中的各种有趣的定理，如Demailly和Rashkovskii比较定理。我们还完成了Lagerberg开始的工作的积极封闭的超电流的程度，我们证明了一个可去奇点的结果为积极的超电流。
英文摘要：
The goal of this work is to extend the concepts of generalized Lelong number of positive currents investigated by Skoda, Demailly and Ghiloufi in complex analysis, to weakly positive supercurrents on the real superspaces. We generalize then a result of Lagerberg when the supercurrent is closed as well as a very recent result of Berndtsson for minimal supercurrents associated to submanifolds of $\mathbb{R}^n$. The main tool is a variant of the well-known Lelong-Jensen formula in the superformalism case. Moreover, we extend to our setting various interesting theorems in complex analysis such as Demailly and Rashkovskii comparison theorems. We also complete the work begun by Lagerberg on the degree of positive closed supercurrents and we prove a removable singularities result for positive supercurrents.
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