2020/11/19 by Fredj Elkhadhra, Elkhadhra, Fredj, Khalil Zahmoul +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV
paper · pdf · doi:10.48550/arxiv.2011.09668
This is the second version of the paper. We added new results and we improved the presentation of the article
arxiv created 2021/10/24 · arxiv updated 2021/10/26
In this study, we first define the local potential associated to a weakly positive closed supercurrent in analogy to the one investigated by Ben Messaoud and El Mir in the complex setting. Next, we study the definition and the continuity of the m-superHessian operator for unbounded m-convex functions. As an application, we generalize our previous work on Demailly-Lelong numbers and several related results in the superformalism setting. Furthermore, strongly inspired by the complex Hessian theory, we introduce the Cegrell-type classes as well as a generalization of some m-potential results in the class of m-convex functions.