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Results in Mathematics

, 74:10 | Cite as

m-Generalized Lelong Numbers and Capacity Associated to a Class of m-Positive Closed Currents

  • Fredj ElkhadhraEmail author
Article
  • 36 Downloads

Abstract

In this paper we firstly define the m-generalized Lelong numbers of a m-positive closed current. Secondly, we associate a capacity to a given class of m-positive closed currents. The pluripolarity and the quasicontinuity of m-subharmonic functions with respect to such a capacity are investigated. Finally, we introduce the notion of m-generalized Lelong numbers of a given class of m-positive closed currents and we prove that these numbers can be expressed in terms of the capacity previously defined.

Keywords

m-Subharmonic functions positive currents capacity 

Mathematics Subject Classification

32W50 32C30 31A15 

Notes

Acknowledgements

The author would like to thank the referee for his/her remarks and suggestions which helped to improve the presentation of the paper.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Département de MathématiqueEcole Superieure des Sciences et de la Technologie de Hammam SousseHammam SousseTunisie

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