Existence of Lelong numbers of positive plurisuperharmonic currents

Autor:	Noureddine Ghiloufi
Rok vydání:	2016
Předmět:	010101 applied mathematics Discrete mathematics Comparison theorem Class (set theory) Current (mathematics) Plurisubharmonic function General Mathematics Existential quantification 010102 general mathematics Open set 0101 mathematics 01 natural sciences Mathematics
Zdroj:	Bulletin des Sciences Mathématiques. 140:64-81
ISSN:	0007-4497
DOI:	10.1016/j.bulsci.2014.12.007
Popis:	In this paper, we prove that if T is a positive plurisuperharmonic current of bidimension ( p , p ) on an open set Ω of C n , 0 p n , then there exists a pluripolar subset E T of Ω such that the Lelong number ν T ( z ) of T at z exists for every z ∈ Ω ∖ E T . We give an example to show that the exceptional subset E T is non-empty in general. Furthermore, we prove a comparison theorem for this class of currents and we conclude that this number is independent of the system of coordinates.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::cebe4afae0028c358bc90feb2ecc202e https://doi.org/10.1016/j.bulsci.2014.12.007 Zobrazit plný text záznamu Full Text from ScienceDirect