$m$-potential theory and $m$-generalized Lelong numbers associated with $m$-positive supercurrents

Fredj Elkhadhra; Khalil Zahmoul

$m$-potential theory and $m$-generalized Lelong numbers associated with $m$-positive supercurrents

Complex Variables 2021-10-26 v2

Authors: Fredj Elkhadhra , Khalil Zahmoul

Abstract

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.

Cite

@article{arxiv.2011.09668,
  title  = {$m$-potential theory and $m$-generalized Lelong numbers associated with $m$-positive supercurrents},
  author = {Fredj Elkhadhra and Khalil Zahmoul},
  journal= {arXiv preprint arXiv:2011.09668},
  year   = {2021}
}

Comments

This is the second version of the paper. We added new results and we improved the presentation of the article

$m$-potential theory and $m$-generalized Lelong numbers associated with $m$-positive supercurrents

Abstract

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