2018/09/04 by Fredj Elkhadhra, Elkhadhra, Fredj, Khalil Zahmoul +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.CV
paper · pdf · doi:10.48550/arxiv.1809.00992
27 pages. This is the second version of the paper. We added new results and replaced the last section with a new one
openalex publication_date 2018/09/04 · arxiv created 2019/09/19 · arxiv updated 2019/09/20 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
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 ℝn. 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.